Elastomeric Foam Systems for Novel Mechanical Properties and Soft

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ELASTOMERIC FOAM SYSTEMS FOR NOVEL MECHANICAL PROPERTIES AND SOFT

ROBOT PROPRIOCEPTION

A Dissertation

Presented to the Faculty of the Graduate School

of Cornell University

In Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Ilse Mae Van Meerbeek

December, 2018

ELASTOMERIC FOAM SYSTEMS FOR NOVEL MECHANICAL PROPERTIES AND SOFT

ROBOT PROPRIOCEPTION

Ilse Mae Van Meerbeek, Ph.D.

Cornell University 2018

Soft materials have enabled the fabrication of novel robots with interesting and complex capabilities. The same properties that have enabled these innovations—continuous deformation, elasticity, and low elastic moduli—are the same properties that make soft robotics challenging.

Soft robots have limited load-bearing capabilities, making it difficult to use them when manipulation of heavy objects is needed, for example. The ability for soft robots to deform continuously makes it difficult to model and control them, as well as impart them with adequate proprioception. This dissertation presents work that attempts to address these two main challenges by increasing load-bearing ability and improving sensing.

I present a composite material comprising an open-cell foam of silicone rubber infiltrated with a low melting-temperature metal. The composite has two stiffness regimes—a rigid regime at room temperature dominated by the solid metal, and an elastomeric regime at above the melting temperature of the metal, which is dictated by the silicone. I characterize the mechanical properties of the composite material and demonstrate its ability to hold different shapes, self-heal, and actuate using shape memory.

In an advance for soft robotic sensing, I present a silicone foam embedded with optical fibers that can detect when it is being bent or twisted. I applied machine learning techniques to the diffuse reflected light exiting the optical fibers to detect deformation as well as predict the magnitude of that deformation. The best models predicted the angle of bend and twist with a mean absolute error of 0.06 degrees. However, the model accuracy decreases with time due to drift of the constitutive optical fiber light intensity values. I lastly present research that reduces model error due to sensor drift using data augmentation.

BIOGRAPHICAL SKETCH

Ilse was born in San Francisco, California, where she spent her childhood and adolescence, and where she attended The Hamlin School. After Hamlin, she attended St. Paul’s School in Concord,

New Hampshire. She spent her junior year abroad in Rennes, France on a study-abroad program called School Year Abroad. Ilse received her B.A. in Mathematics from Amherst College in

Amherst, Massachusetts. While an undergraduate, she also took many courses in Physics and

Computer Science and was an athlete on the rowing team. After college, Ilse lived in Cambridge,

Massachusetts, where she worked in web development and pursued her dreams of being an elite competitive rower. Ilse enrolled at Cornell University in 2013, completed her qualifying exam in

January 2015, and received her M.S. in Mechanical Engineering in August 2016. She has also taken advantage of the myriad activities Cornell has to offer and has learned a bit of rock-wall climbing, springboard diving, and has taken up cycling.

DEDICATION

To my mom, Madelyn Van Meerbeek, who taught me the value of asking “why?”, and to all the

other women who have been mothers to me: Teryl, Trish, Julia, Rosemary, and Catherine.

ACKNOWLEDGMENTS

I would like to thank my PhD advisor, Professor Rob Shepherd, for his technical guidance, his willingness for me to explore new topics, his investment in my success as a student while supporting my emotional wellbeing as a person, and for his belief in me. I also would like to thank my three committee members: I thank Professor Hadas Kress-Gazit for her technical guidance and for making me feel welcome at Cornell, Professor Meredith Silberstein for her help with mechanical testing and analysis, and Professor Guy Hoffman for his inspiration and technical guidance.

I also thank my lab mates Bryan, Chris, Ben, Huichan, Kevin, Shuo, T.J., Lillia, James, Cameron,

Patricia, Maura, Autumn, Ronald, Jose, Yaqi, Zheng, and Kaiyang for their support, encouragement, and friendship.

I would like to thank Marcia Sawyer and Joe Rogan for their help with all things administrative, helping me navigate life as a graduate student.

I also thank the professors whose inspiring, fun, and instructive courses I have taken while here at

Cornell. Specifically, I would like to thank Andy Ruina, Kilian Weinberger, Chris De Sa, Guy

Hoffman, Rob Shepherd, and Brian Kirby.

I would also like to thank my closest friends, Alex, Stef, Claire, Caitlin, Disha, and Liz, for encouraging me, giving me advice, dropping everything and coming to visit me when I needed it most, and being amazing, talented women who inspire me every day.

I would lastly like to thank my husband, Jon, for his love and support. As a fellow graduate student in Mechanical Engineering, he experienced every important step with me, encouraged me, and helped me understand and solve engineering questions throughout our time here.

TABLE OF CONTENTS

BIOGRAPHICAL SKETCH ...... iv DEDICATION ...... v ACKNOWLEDGMENTS ...... vi TABLE OF CONTENTS ...... vii LIST OF FIGURES ...... ix LIST OF TABLES ...... xii CHAPTER 1: INTRODUCTION ...... 1 1.1 Soft Robotics Overview ...... 1 1.2 Challenges in Soft Robotics ...... 6 1.3 Dissertation Scope and Organization ...... 6 1.4 Related Work ...... 8 CHAPTER 2: MORPHING METAL AND ELASTOMER BICONTINUOUS FOAMS FOR REVERSIBLE STIFFNESS, SHAPE MEMORY, AND SELF-HEALING SOFT MACHINES13 2.1 Introduction ...... 13 2.2 Materials and Methods ...... 14 2.3 Results ...... 17 2.4 Conclusion ...... 23 2.5 Supporting Information ...... 24 CHAPTER 3: SOFT OPTOELECTRONIC SENSORY FOAMS WITH PROPRIOCEPTION . 29 3.1 Introduction ...... 29 3.2 Materials and Methods ...... 32 3.3 Results ...... 38 3.4 Discussion ...... 44 CHAPTER 4: COMPARING HYPERPARAMETER OPTIMIZATION TECHNIQUES FOR DATA AUGMENTATION TO FIX SENSOR DRIFT IN A SOFT ROBOTIC SENSOR...... 50 4.1 Introduction ...... 50 4.2 Related Work ...... 51 4.3 Experiments ...... 53 4.4 Results ...... 55 4.5 Discussion ...... 59 4.6 Future Work ...... 62 4.7 Conclusion ...... 62

vii

CHAPTER 5: CONCLUSIONS ...... 63 5.1 Summary of Contributions and Future Work ...... 63 APPENDIX A: POROELASTIC FOAMS FOR SIMPLE FABRICATION OF COMPLEX SOFT ROBOTS ...... 66 A.1 Introduction ...... 66 A.2 Materials & Methods ...... 68 A.3 Results & Discussion ...... 71 A.4 Conclusions ...... 77 A.5 Experimental Section ...... 78 A.6 Supplemental Information ...... 79 APPENDIX B: SCULPTING SOFT MACHINES ...... 86 B.1 Introduction ...... 86 B.2 Materials and Methods ...... 87 B.3 Results & Discussion ...... 97 B.4 Conclusions ...... 103 APPENDIX C: FIBER SELECTION FOR ADDRESSING SENSOR DRIFT IN AN OPTICAL, PROPRIOCEPTIVE FOAM ...... 104 C.1 Introduction ...... 104 C.2 Experiments ...... 104 C.3 Results ...... 105 C.4 Discussion ...... 105 REFERENCES ...... 107

viii

LIST OF FIGURES

Figure 1.1 Examples of Soft Materials in Living Organisms...... 2

Figure 1.2 Examples of Soft Robot Locomotion...... 3

Figure 1.3 Examples of Soft Robot Manipulation...... 4

Figure 1.4 Examples of Soft Robotic Sensors...... 5

Figure 1.5 Foams in Soft Robotics...... 8

Figure 1.6 Elastomer-Based Composites...... 9

Figure 1.7 Proprioception in Soft Robots...... 10

Figure 1.8 Data-Driven Models for High-Level Sensing in Soft Robots...... 11

Figure 2.1 Foam close-ups and demo...... 15

Figure 2.2 Channel outgas setup...... 16

Figure 2.3 Mechanical testing of foam and composite...... 18

Figure 2.4 Mechanical testing data for sealed samples...... 19

Figure 2.5 Composite morphing...... 21

Figure 2.6 Composite under stress...... 22

Figure 2.7 Welding and self-healing...... 23

Figure 2.8 Mechanical data for repeated healed sample...... 28

Figure 3.1 Foam assembly design...... 31

Figure 3.2 Sensor functionality...... 33

Figure 3.3 Experimental setup...... 35

Figure 3.4 Gathering data...... 36

Figure 3.5 Results from k-fold cross-validation...... 40

Figure 3.6 Effect of training data size...... 43

Figure 3.7 Effect of feature set size...... 45

Figure 3.8 Random vs. greedy feature removal...... 46

Figure 4.1 Sensor Drift...... 52

Figure 4.2 Grid Search vs. Random Search vs. Bayesian Optimization...... 56

Figure 4.3 Random Search vs. Bayesian Optimization...... 57

Figure 4.4 Augmented Model Performance on Test Data...... 58

Figure 4.5 Training a New Model on Modified Data vs. New Data...... 59

Figure A.1 Foam-based pneumatic actuation...... 67

Figure A.2 Tensile and blocked force measurements...... 70

Figure A.3 Airflow through foam actuators...... 73

Figure A.4 The foam-based fluid pump design and principle of operation...... 75

Figure A.5 Thermogravimetric analysis of foam components...... 79

Figure A.6 Blocked force behavior of bending actuators...... 80

Figure A.7 Image analysis of µCT images...... 82

Figure A.8 Molding process to form the pump’s foam shell...... 84

Figure A.9 Airflow measurement of soft foams and a pneu-net model...... 85

Figure B.1 Fabrication of foam forms...... 88

Figure B.2 Porous structure of elastomer foam...... 89

Figure B.3 Mechanical testing and airflow measurements...... 90

Figure B.4 Airflow measurement experimental set-up...... 91

Figure B.5 Rheological behavior of liquid foam precursor...... 93

Figure B.6 Foam actuators with different sealing materials and methods...... 95

Figure B.7 Actuation force measurement...... 96

Figure B.8 Sealing process for foam actuators...... 98

Figure B.9 Blocking force measurements setup...... 99

Figure B.10 Bending Actuator Performance...... 100

Figure B.11 Apple picking with a sculpted, Y-shaped gripper...... 102

Figure C.1 Model Error on Drifted Data vs. Feature Set Size...... 106

LIST OF TABLES

Table 2.1 Data from repeated welding experiment...... 16

Table 3.1 Model parameters for best prediction models...... 38

Table 3.2 Classifier model error rate...... 39

Table 3.3 Single-output regression model errors...... 39

Table 3.4 Multi-output regression model errors...... 39

Table 3.5 Model evaluation times...... 48

Table 4.1 Validation Errors for Best Models...... 55

Table 4.2 Test Errors for Best Augmented Models...... 57

Table 4.3 Validation Error vs. Test Error...... 58

Table 4.4 Data Augmentation vs. Data Shifting...... 58

Table B.1 Mechanical properties according to manufacturers’ datasheets...... 92

xii

CHAPTER 1

INTRODUCTION

1.1 Soft Robotics Overview

1.1.1 Definition

Soft Robotics is the subfield of robotics that uses mechanisms and sensors composed primarily from compliant materials, such as elastomers, gels, and fluids1–3. This compliance can originate from either intrinsic (i.e., low elastic modulus) or extrinsic (i.e., low stiffness) material properties. Their materials and mechanics often mimic those found in living organisms.

1.1.2 Motivation

The first “soft” actuators appeared in the 1950’s, with the McKibben actuator4,5; however, the field of soft robotics started to gain real momentum in the 1990’s when researchers encountered problems that rigid materials alone could not solve6,7. Rigid robots are very good at performing specific tasks with high speed, accuracy, and repeatability8,9; however, those systems often lack adaptability, can be complex, are not resilient under collision, and are often unsafe for human interaction10,11. To address some of these issues, roboticists have sought alternative solutions using two main approaches: improving robots’ “brains” and improving their “bodies”. Some researchers have addressed the issues of adaptability and human-safety by improving low-level controllers12–

14 or developing high-level behavior and planning algorithms15,16. Others have noted how living organisms benefit from soft tissues (Figure 1.1) and have chosen to emulate those biological materials.

Soft materials can be used to fabricate novel robotic hardware with several new capabilities. Since inherently compliant materials deform continuously, they can conform to

unpredicted structures and objects17 to traverse18,19 or manipulate20,21 them, respectively. Also, they can be used to fabricate simple structures that perform complex motions22–24. Comparable versatility with traditional materials requires the robot to be very complex25. Additionally, elastomeric materials elastically deflect easily and reversibly under stress, protecting soft robotic components from plastic damage7,19, as well as being safer for human interaction26.

Figure 1.1 Examples of Soft Materials in Living Organisms. Adapted from “Soft Robotics: Biological Inspiration, State of the Art, and Future Research” by Deepak Trivedi, Christopher D. Rahn, William M. Kier, and Ian D. Walker1

1.1.3 State-of-the-Art

Currently, soft robots have achieved exciting capabilities in locomotion and manipulation,

many of which have been inspired by living organisms. For example, researchers replicated the caterpillar’s ability to roll by using silicone rubber and shape memory actuation27. Shape memory alloys have also been used to fabricate artificial earthworms made of flexible mesh materials28

(Figure 1.2e) and silicone29. Tendon-driven actuation30–32 has been employed to drive an artificial octopus arm made of silicone and braided wire. Roboticists have also fabricated an artificial silicone fish33,34 (Figure 1.2l) that employs hydraulic actuation. The field of soft robotics has also achieved legged locomotion through pneumatic actuation18,19, (Figure 1.2b-d) and jumping through combustion35 (Figure 1.2j).

Figure 1.2 Examples of Soft Robot Locomotion. Adapted from “Design, Fabrication, and Control of Soft Robots” by Daniela Rus and Michael T. Tolley3. In the area of soft robot manipulation, researchers have developed pneumatically actuated grippers that use the continuous deformation experienced by elastomeric materials to grip a variety of objects20,32,36,37 (Figure 1.3d). Grippers based on granular jamming have also demonstrated versatile gripping capabilities21,38 (Figure 1.3c). The human hand has inspired many artificial robotic hands capable of sensing texture39, grasping a variety of objects20,40, identifying objects41, and gripping with high force and speed42.

Figure 1.3 Examples of Soft Robot Manipulation. Adapted from “Design, Fabrication, and Control of Soft Robots” by Daniela Rus and Michael T. Tolley3 Soft robotic technology has also found use in prosthetics and assistive devices. Researchers have used electromyography (EMG) signals in the forearms of patients to control soft robotic gloves that enhance the force output of the human hand43,44. Soft roboticists have developed gloves that have enabled paralyzed patients to grasp every-day objects45 and assisted with the rehabilitation of patients who have lost partial function of their hands46,47 (Figure 1.3i). Soft materials have also been successfully applied to devices for gait assistance in humans48 and rodents49.

In addition to new mechanical capabilities, researchers have made great progress in developing soft robotic sensors. With these new technologies, soft robots can detect strain and pressure in a variety of ways. Some researchers have developed strain and pressure sensors by fabricating electrically conductive, soft channels embedded in insulating soft materials and

measuing electrical resistance as the channel cross-sectional area and length change with deformation. These types of soft sensors have been fabricated using conductive materials such as low melting temperature metals50–53 and carbon black54,55 (Figure 1.4a,b). Researchers have also developed capacitance-based sensors. They have demonstrated that one can fabricate soft parallel- plate capacitors using dielectrics such as silicone rubber, and conductive soft materials such as hydrogels56–58 (Figure 1.4c). Both elastomeric and plastic optical fibers have also been employed to detect strain, curvature, and pressure39,59,60 (Figure 1.4d,e). These sensors can have applications in soft robotics and wearable electronics, and can serve as more sensitive, human-friendly skins for rigid robots.

Figure 1.4 Examples of Soft Robotic Sensors. Adapted from (a) “Design and fabrication of soft artificial skin using embedded microchannels and liquid conductors” by Y. L. Park et al.53 (b) “Embedded 3D printing of strain sensors within highly stretchable elastomers” by J. T. Muth et al.54 (c) “Ionic Skin” by J. Yun et al.58 (d) “Optoelectronically innervated soft prosthetic hand via stretchable optical waveguides” by H. Zhao et al.39 (e) “Highly stretchable optical sensors for pressure, strain, and curvature measurement” by C. To et al.60

1.2 Challenges in Soft Robotics

Complaint materials enable many new functionalities, but also present several challenges.

Soft robots have limited load-bearing capability due to the low elastic moduli of the constitutive materials as well as the current limitations in fabrication techniques61. It also remains difficult to consistently manufacture reliable soft actuators, which results in frequent mechanical failure and varied performance between actuators.

Another major challenge is modelling the configuration of soft robots. Rigid robots have a finite number of degrees of freedom, and therefore require a finite number of parameters (e.g. joint angles and linkage lengths) to model them. Since soft materials deform continuously, they have infinite passive degrees of freedom, which makes modelling soft robotic structures much slower and more challenging than modelling their rigid counterparts3.

Additionally, the state-of-the-art sensors remain crude in that they can only sense certain types of deformation over relatively large regions of a soft robot body (e.g. curvature of an actuator, pressure at a robotic fingertip). Due to the low density of sensor distributions present in current soft robot designs, they cannot detect arbitrary deformation, and thus they do not have complete proprioception. This lack of good models and comprehensive sensing leads to difficulty in control.

1.3 Dissertation Scope and Organization

This dissertation presents work using elastomeric foams to address two of the current challenges in soft robotics: increasing load-bearing capability and improving sensing.

In chapter 2, I present a composite of two interpenetrating foams—an elastomer and a low melting temperature metal alloy. At room temperature, the metal is stiff, and the composite is load-

o bearing; however, at above the melting temperature of the metal (Tm = 62 C), the composite is

highly extensible and resilient. This chapter demonstrates this composite’s use for shape changing structural supports and shape memory actuation. Additionally, by melting and freezing the metal foam, the composite can both self-heal and be assembled into larger structures from smaller subcomponents.

In chapter 3, I present an internally illuminated elastomer foam that has been trained to detect its own deformation through machine learning techniques. Optical fibers transmit light into the foam and simultaneously receive diffuse waves from internal reflection. Machine learning techniques interpret the diffuse reflected light to predict whether the foam is being twisted clockwise, twisted counterclockwise, bent up, or bent down. Machine learning techniques were also used to predict the magnitude of the deformation type. On new data points, the best model predicted the type of deformation with 100% accuracy, and the magnitude of the deformation with a mean absolute error of 0.06 degrees.

The models for the optical sensor in chapter 3 have very good performance initially; however, the values for the embedded optical fibers drift with time, causing a dramatic increase in error. In chapter 4, I present an attempt to address this performance decline by applying data augmentation to reduce the error. I augment the trainings data by duplicating it and adding an offset value to each constitutive sensor value (feature) in the duplicate set. Finding the 30 optimal values requires searching through k30 possible augmentation parameter sets where k is the number of considered values. Given this large parameter space, I compare three different hyperparameter search techniques: grid search, random search, and Bayesian optimization. Random search found the best models during validation, but Bayesian optimization found the best model when tested on new, unobserved data. Using the best model found with Bayesian optimization, the average regression test error was reduced from 25° to 16°.

1.4 Related Work

1.4.1 Elastomeric, Open-Cell Foams for Soft Robots

Solid foams, or cellular solids, are clusters of small, enclosed spaces (i.e. pores) whose boundaries are defined by interconnected networks of solid struts62. The pores in a completely closed-cell foam are isolated with no overlap. The pores in open-cell foams—also known as reticulated foams—do overlap, have a high surface area to volume ratio, and have low densities.

Their high surface area and porosity enable their use as filters and absorbers, permit the flow of liquids or gasses, and can be used to fabricate interpenetrated composite materials63. Open-cell foams made of rigid materials can be low-density while still being stiff and strong, making them useful for certain structural applications64. Open-cell elastomeric foams are highly compressible, can have Poisson’s ratios close to zero, and have a nonlinear mechanical response with multiple regimes62.

Some of these characteristics have been exploited to benefit soft robotics. An open-cell elastomeric foam can define and hold the shape of a pneumatic chamber with elastomeric walls while still allowing air flow.

Mac Murray et al.24 used this feature to fabricate soft, 3-dimensional actuators with complex shapes, and Argiolas et al. presented Figure 1.5 Foams in Soft Robotics. Adapted from hand-sculpted soft actuators made of silicone (a) “Poroelastic Foams for Simple Fabrication of Complex Soft Robots” Mac Murray et al.24 (b) foam65 (Figure 1.5a-b). Using foams also “Sculpting Soft Machines”, by Argiolas et al. 65 (c) “An Any-Resolution Distributed Pressure simplifies soft actuator fabrication by not Localization Scheme Using a Capacitive Soft Sensor Skin”, by Sonar et al.69 requiring that channels be specifically

patterned65,66. In addition to their use in actuators, elastomeric foams—with their low density and high compressibility—have been employed as the dielectric layer in soft capacitive sensors67–70

(Figure 1.5c) and in optical tactile sensors71.

1.4.2 Elastomer-Based Composite Materials

Researchers have combined several types of materials with elastomers to enhance their capabilities. Elastomers are typically not electrically conductive; however, stretchable conductors have been fabricated72 by embedding them with conductive materials in the form of particles73–76,

“wavy” channels77,78, and liquid79 (Figure 1.6a-b). To increase load-bearing capability in elastomers, engineers have combined them with low melting temperature metal80,81 and thermopastics82–86, to form composite materials with two different, thermally accessible stiffness regimes—rigid and stretchable (Figure 1.6c-d).

Figure 1.6 Elastomer-Based Composites. Adapted from (a) “A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates”, by Khang et al.78 (b) “Masked Deposition of Gallium‐Indium Alloys for Liquid‐Embedded Elastomer Conductors”, by Kramer et al.79 (c) “Soft matter composites with electrically tunable elastic rigidity”, by Shan et al.80 (d) “Thermoplastic variable stiffness composites with embedded, networked sensing, actuation, and control”, by McEvoy et al.82

1.4.3 Proprioception in Soft Robots

For soft robots to achieve truly adaptive functionality, they must be reliably controlled,

which requires them to have good proprioception. Soft roboticists have embedded sensors into their devices to give them some knowledge of their configuration. Lossy plastic optical fibers have enabled curvature control of a soft hand orthosis44 (Figure 1.7a); stretchable optical fibers have given soft actuators knowledge of curvature, actuation, and pressure at specific points39,42 (Figure

1.7b). Optical sensing has also been used to give soft, plush items knowledge of their deformation87

(Figure 1.7c). Marchese et al.88,89 used the piecewise constant curvature90 (PCC) assumption to calculate the forward and inverse kinematics of a soft fluidic actuator manipulator based on actuator pressure.

Figure 1.7 Proprioception in Soft Robots. Adapted from (a) “A helping hand: Soft orthosis with integrated optical strain sensors and EMG control”, by Zhao et al.44 (b) “Optoelectronically innervated soft prosthetic hand via stretchable optical waveguides”, by Zhao et al.39 (c) “Detecting Shape Deformation of Soft Objects Using Directional Photoreflectivity Measurement”, by Sugiura et al.87

1.4.4 Algorithmic Solutions for Soft Robots

For a robot to be autonomous and able to perform complex tasks, it must perceive its environment, know its own physical state, and make decisions resulting in actuation and motion.

Soft robotics, until now, has necessarily focused on the development of novel soft robotic hardware. At this point, however, soft robotic hardware has become advanced enough that researchers have begun controlling soft robot actuation, developing soft robotic devices that respond to high-level commands, and optimizing soft robotic behavior.

Researchers have applied several forms of control algorithms to control soft robot actuation. Zhao et al.91 implemented a curvature control algorithm using a gain-scheduled PID

controller, Marchese et al.88 used a cascaded PI and PID control algorithm to control the curvature of fluidic actuator segments of a soft manipulator. Calli and Dollar used visual feedback for precision manipulation with an underactuated hand with elastic joints92 and applied model

Predictive Control (MPC) to improve the accuracy of that hand93. Best et al. also used MPC to control a soft, pneumatically actuated humanoid robot with 14 degrees of freedom94.

Soft roboticists have also implemented algorithms that allow a soft robot to track its manipulator’s path through space16,88, optimize its manipulator’s trajectory89, and synthesize gaits for more adaptability95. Alterovitz et al. developed a motion planning algorithm based on a Markov

Decision Process that steers a flexible needle for minimally invasive surgery96.

Figure 1.8 Data-Driven Models for High-Level Sensing in Soft Robots. Adapted from (a) “A Deformable Interface for Human Touch Recognition using Stretchable Carbon Nanotube Dielectric Elastomer Sensors and Deep Neural Networks”, by Larson et al.97 (b) “Haptic Identification of Objects using a Modular Soft Robotic Gripper”, by Homberg et al.41

Due to the complex ways in which soft materials can deform, (pinching, twisting, stretching, etc.) roboticists have also turned to algorithms for interpreting sensory data and modelling soft robot dynamics. Larson et al.97 developed the OrbTouch—an elastomer device that uses Neural Nets (or Multi-Level Perceptions) to recognize different types of gestures. They used this gesture recognition capability to control a game of Tetris®. Homberg et al. used a clustering algorithm to identify objects grasped by a soft gripper based on its configuration during the grasp41.

Thuruthel et al. implemented recurrent neural networks to learn the dynamical model of a soft robotic manipulator and successfully implemented open loop predictive control with the learned model98. Similarly, Gillespie et al. implemented deep neural nets to learn soft robot dynamical models and implemented MPC to demonstrate their utility99.

To achieve the performance and adaptability that we observe in living organisms, soft robotics will need to continue advancing its hardware and software solutions. This dissertation presents novel capabilities in both areas.

CHAPTER 2

MORPHING METAL AND ELASTOMER BICONTINUOUS FOAMS FOR REVERSIBLE

STIFFNESS, SHAPE MEMORY, AND SELF-HEALING SOFT MACHINES*

2.1 Introduction

Synthetic composites usually have fixed internal structures and mechanical properties tuned for a particular application. Natural composite materials, however, can alter their structures and mechanical properties in response to changing environmental conditions. Bone, for example, remodels itself upon induced mechanical stresses.100,101 When touched, the sea cucumber can rapidly and reversibly increase the stiffness of its skin for protection.102,103 Here we present a synthetic composite material that demonstrates some of these abilities: stiffness variation and shape morphing.

Recent work on variable stiffness composites based on inducing phase changes in polymers82–86 and metals80,81 has begun to show promise in overcoming the usual tradeoff between shape adaptability and load-bearing capability. These synthetic materials are often layered composites86 or contain soft microchannels filled with a low melting temperature material;80,84 when this phase change material is molten, the composite can be easily deformed. Such structures are highly sensitive to cracks in the stiff material and their need for specialized, directed assembly results in anisotropic mechanical properties. In this communication, we describe the material design and simple processing of a bicontinuous104 network of two foams—elastomeric and

metallic. The metal (an alloy of indium, tin, and bismuth) melts at 푇 = 62 퐶. When the

* Van Meerbeek, I. M., Mac Murray, B. C., Kim, J. W., Robinson, S. S. Zou, P. X., Silberstein, M. N., and Shepherd, R. F. (2016) Morphing Metal and Elastomer Bicontinuous Foams for Reversible Stiffness, Shape Memory, and Self-Healing Soft Machines. Advanced Materials. Reproduced with permission. 13

composite’s temperature is below 푇 , the mechanical properties of the solid metal foam

dominate, and the material is stiff; above 푇 , the metal is molten, and the elastomer foam dictates the composite’s mechanical properties, making the composite rubbery. The silicone foam acts as an entropic spring105 that stores potential energy through foam deformation followed by freezing of the metal; upon re-melting the metal, the elastomer returns to its initial shape. In this paper, we demonstrate five capabilities of this bicontinuous foam composite: (i) reversible stiffness, (ii) an ability to change shape by stretching to over 200% strain when heated, (iii) shape memory actuation,106–108 (iv) non-autonomic, heat-triggered self-healing,109,110 and (v) assembly into larger continuous structures from smaller sub-components.

2.2 Materials and Methods

We chose eutectic Sn-Bi-In (Field’s Metal, RotoMetals) as the metal for its low melting temperature, low toxicity, and high elastic modulus (퐸 ≅ 9.25 퐺푃푎)80 at room temperature.

To allow a large range of shape morphing with little resistance to deformation, we used a silicone elastomer (Elastosil® M4600, Wacker) for our matrix material due to its large strain to failure,

61 휀 ~ 8.0, and low elastic modulus, 퐸 = 0.54 푀푃푎 ; additionally, silicone is stable over the temperature range required to melt the metal alloy.35,111

To fabricate this bicontinuous structure, we formed an open-cell network of pores in silicone (average diameter of 2 mm) (Figure 2.1a) via dissolution of a densely packed fugitive salt.112 We then impregnated the silicone foam’s open-cell network with molten metal (Figure

2.1b) using a microfluidic channel outgas technique (Figure 2.2).113 This process produces uniformly distributed, interpenetrating stochastic networks of Field’s metal and silicone, resulting in an isotropic composite that can be cut or molded into a variety of 3-dimensional geometries.

See Supporting Information (SI) for more details about this procedure.

Figure 2.1 Foam close-ups and demo. (a) Silicone foam, (b) imbibed with Field’s metal. Composite under 500 g bending stress at (c) ~23 °C and (d) > 푇 .

At above 푇 , the molten metal remains within the elastomeric foam even during deformation and contact with other composite surfaces. This strong impregnation is likely due to surface oxidation of the liquid metal, which adheres strongly to the silicone surface.114,115 As the molten metal is now in contact with its own oxide, strong surface wetting results in high capillary forces. Table 2.1 shows the results of an experiment conducted to demonstrate the strong capillary forces (see SI text for more details).

Figure 2.2 Channel outgas setup. Acrylic container used to submerge silicone foam into molten metal bath with foam sample at center. Although some commercially available elastomer foams exist, the selection is limited and tends to contain primarily small-pore or closed cell foams that have lower ultimate strains and higher elastic moduli than our selected silicone material. As we found that large pore sizes ease infiltration of the metal and we require an open cell foam network, we chose to form our own foams using the lost salt method with large grained salt (i.e., “Himalayan”, Pure Himalayan Salt).

While directly 3D printing the pore network could enable precision control of the composite architecture, our stochastic process is simple, easily duplicated, and results in an isotropic structure.

Step Number Sample #1 Mass (g) Sample #2 Mass (g) Fused Mass (g) 0 48.92 43.94 - 1 - - 92.86 2 48.75 44.11 - 3 - - 92.85 4 48.56 44.30 - 5 - - 92.85 6 48.56 44.31 - 7 - - 92.85 Table 2.1 Data from repeated welding experiment.

Controlling pore size and porosity allows us to tune the properties of our composite. For example, increasing the silicone porosity would result in a lower average cross-sectional area of the silicone and a higher average cross-sectional area of the metal. In this case, the effective elastic

modulus of the silicone foam would decrease, and the overall elastic modulus of the composite foam would increase. Presently, we have chosen an intermediate elastomer foam porosity (50%); however, 3D printing strategies could increase this porosity even further and result in stronger metal foams that would likely only improve the self-healing and welding capabilities of the composite. If the pores become too large, however, the capillary forces retaining the molten metal may become insufficient. Alternatively, increasing the volume fraction of elastomer in the composite will increase the composite’s restoring force for shape memory actuation.

For mechanical testing, we molded dumbbell and cylindrical specimens using ASTM D412

– 06a(2013) and ASTM E9-09 standards respectively. We imbibed half of the samples and measured the mechanical properties of the resultant pure elastomer foams and composites by conducting uniaxial, monotonic tension and compression tests on a Zwick & Roell Z010 testing system according to the aforementioned ASTM standards (Figure 2.3). (See SI for more details.)

For reference, we tested sealed samples of empty elastomer foam and the foam imbibed with molten metal and found that the mechanical properties were nearly identical (Figure 2.4); therefore, we present here only the empty elastomer foam. We note here that the mechanical properties of the sealed samples do not match those in Figure 2.3, left; this difference is likely due to silicone degradation as a result of salt exposure over the extended periods between testing.116

2.3 Results

Bars (2.5 cm x 11.7 cm x 1.1 cm) of the composite sustained bending loads of 0.5 kg without noticeable deflection (Figure 2.1c); upon melting of the metal, the bars immediately yielded (Figure 2.1d). Tensile testing data (Figure 2.4; SI Text) show that at room temperature the

composite has an elastic modulus of 퐸 ~1.8 푀푃푎 (measured at strains 0.01 < 휀 < 0.03)

which reduces to 퐸 ~0.1 푀푃푎 (0.20 < 휀 < 0.40) at 푇 > 푇 . The compression testing

data (Error! Reference source not found., right) show similar results, with 퐸 ~3.1 푀푃푎

(0.01 < 휀 < 0.03) at room temperature and 퐸 ~0.1 푀푃푎 at 푇 > 푇 (0.20 < 휀 < 0.40).

Figure 2.3 Mechanical testing of foam and composite. Tension (left) and compression (right) on two different stress scales.

The composite has two functional mechanical states: stiff and compliant. Exploiting the dramatic variance in mechanical properties, we morphed the composite structures by heating them to ~70 °C, deforming them into bent, twisted, and elongated shapes, then allowing them to cool

below 푇 to freeze the material into these configurations (Figure 2.5a-d). Due to the

incompressibility of the elastomer, at above 푇 , the total pore volume does not change during 18

tensile loading and therefore the molten metal reorients with the foam structure (Figure 2.6a-b).

We note, however, that during significant compression, when buckling of the elastomer foam matrix occurs,117 the pore volume decreases, forcing the molten metal out of the elastomer matrix

(Figure 2.6c-d). In situations where significant compression was expected to occur, we sealed the composite with a thin (~2-3 mm) silicone skin (Figure 2.4).

Figure 2.4 Mechanical testing data for sealed samples. Silicone foam vs. the composite (a) at room temperature and (b) above 푇 .

The elastomer foam is highly resilient; after morphing, it will return to its initial configuration when the metal is molten and mechanical stresses are removed. We took advantage of the silicone’s resilience to enable shape memory actuation (Video 2.1). As a demonstration, we morphed a rectangular cuboid (27 mm x 27 mm x 9 mm) into a cylinder (diameter, d= 25 mm;

Figure 2.5E, left). By heating the composite to above 푇 , the metal melts and the elastomer foam relaxes and returns to its cuboid form (Figure 2.5E, right). When the strain of the elastomer foam remains below 휀 ~ 2.5 (Figure 2.3,left), the force at a given strain is linearly proportional to

퐸 . Exposed to a stream of hot (500 °C) air, the compressed cube took 78 seconds to recover

89% of its original shape (Video 2.1). By encapsulating a shape memory structure in an elastomer

membrane, we prevented leaking during compression and recovered 100% of the original shape

(Video 2.2).

Since the molten metal can recrystallize with itself, it is possible for cracks in the metal foam to self-heal. We used this ability to heal damaged foam composites. We quantified the results by cutting tensile testing bars in half and rejoining them by melting and refreezing the metal foams

(SI Text). Though the silicone foam does not re-bond, Figure 2.7A shows that the self-healed composite has an elastic modulus that is very close to that of a virgin sample. Self-healed samples also achieve 78% of the undamaged samples’ inelastic limit (measured at 휀=0.04). The decrease in toughness and ultimate tensile strength comes from the irreversible damage done to the elastomer. The severed elastomer foam cannot heal and therefore provides no resistance to deformation; once the metal foam in a healed sample is damaged, the elastomer foam cannot provide structural support as it does in virgin samples. Figure 2.7C-E shows the cutting and healing of a composite bar, where the cut becomes difficult to see after repair—visually demonstrating the remarkable degree of healing achieved.

Figure 2.5 Composite morphing. Morphed configurations that demonstrate the composite’s ability to hold (a) bent, (b) twisted, (c) relaxed, and (d) elongated positions at room temperature. (E, left to right) Compressed cylinder expanding into cuboid through heat.

We conducted mechanical tests on self-healed samples with the worst possible damage: complete severing of the metal and elastomer foams. There are, however, more minor types of damage from which this composite may heal more completely. Most impacts will only damage the metal foam. In such cases, the elastomer foam remains intact and the metal foam can be melted and recrystallized. This material could also suffer puncture damage, where some of the elastomer foam remains intact and able to support load. In this case, self-healing could restore more of the original ultimate toughness.

Using the method for self-healing, we also welded two independent composite pieces into a monolithic structure (Figure 2.7b). Each separate composite surface has both silicone and metal present (Figure 2.1b); thus, when they touch, there is likely metal-metal contact. By heating the two composites while touching, the metallic surfaces mix, and upon freezing, the Field’s metal

recrystallizes into a single form. We measured the mechanical properties of welded samples and compared them to virgin and self-healed ones (Figure 2.7A). The elastic modulus and inelastic limit of the welded samples were nearly identical to those of the self-healed ones. Although cell alignment is not guaranteed in the welded samples, the similar moduli are likely due to the molten metal layer that forms along the cut surface during re-bonding. Remarkably, self-healed and welded surfaces can support loads almost as great as virgin samples before plastically deforming.

As in the self-healed tests, the welded samples exhibited decreased toughness due to damaged elastomer.

Figure 2.6 Composite under stress. Composite bar in tension (a) at room temperature with 0.95 kg and (b) above 푇 with 2.00 kg. Composite bar in compression under a 2.00 kg mass (c) at room temperature and (d) above 푇 .

Figure 2.7 Welding and self-healing. (a) Mechanical testing of self-healed, welded, and virgin composite specimens. (b) Two independent composite samples (left) before welding and (right) after. (c) Composite bar being cut with scissors, (d) damaged composite bar, (e) self-healed composite bar.

2.4 Conclusion

The composite material we designed has a stiffness that can be dramatically varied through changes in temperature. This material can be stretched and reshaped into different rigid structures and can use stored energy in the elastomer to enable shape memory actuation. Under the application of heat, the same composite can self-heal after sustaining damage and can be assembled from a few subcomponents into myriad super-structures with a continuous metal skeletal system.

These capabilities could be used to create multifunctional tools by reforming rigid structures into new shapes, (e.g., a hook into a spear). Like bone, this shape changing capability could also be used to make adjustments to the geometry of a structure in response to its environment. Soft robotic devices such as pneumatically powered elastomer grippers20,61 and quadrupeds18 could benefit from skins of these materials to provide on-demand skeletal networks. 23

The strength and shape adaptability of this class of composites can be improved by employing existing techniques. By using different porogens118 or a 3D printed lost-wax mold,119,120 we could directly control the foam structure and optimize it for various applications. Designing the microstructure such that the metal grains have larger contact areas and therefore fewer areas of stress-concentration would increase the strength. We could also spatially vary the pore structure to form gradient mechanical properties that intentionally induce anisotropic behavior.

Additionally, it is possible that the interpenetration of the metal is not total—future X-ray Μct studies will allow analysis and improvement of the metal foam’s interconnectivity.121 The melting and freezing of the metal in this paper was achieved via external heating; however, the composite’s stiffness can also be controlled via Joule heating the metal directly81 or embedding soft, stretchable heaters80 which will enable shorter melting times. While we report variable stiffness caused by melting and freezing of low melting temperature metal alloys, similar mechanical behavior could be achieved by replacing the phase-changing material—the metal foam—with a thermoplastic one.82–84 With these improvements, shape morphing skeletal networks will enable mechanical structures that can dynamically adapt to changing environments and functional requirements.

2.5 Supporting Information

2.5.1 Silicone Foam Fabrication

We formed the metal-elastomer composite by first mixing equal portions of parts A and B of Elastosil® M4600 together to initiate curing. We immediately added an equal volume of 1-3mm

Himalayan salt crystals (Red Himalayan Crystal Salt, Pure Himalayan Salt). We spread this mixture into a laser-cut acrylic mold and cured it in an oven for 20 minutes at ~85°C. We then de- molded the samples and placed them into a warm water bath until all the salt was dissolved. This required changing the water bath several times to speed up the dissolution process. Once all the

salt appeared to have dissolved, we rung the samples dry by hand and then placed them in the oven to allow all excess water to evaporate. To verify that all the salt had indeed dissolved, we inspected the samples by hand to feel for hard crystals, then measured their mass and compared that number to our recorded silicone mass, which was measured when initially mixing the two-part silicone together.

2.5.2 Composite Fabrication

After fabricating the silicone foam, we heated the samples to ~85°C, then submerged them in a molten bath of Field’s metal also at ~85°C. The metal bath was contained in an acrylic box and the foam was held beneath the surface of the metal by an acrylic grill that was adhered to the walls of the acrylic box (Figure 2.2). With the silicone foam submerged, we placed the metal bath back into the oven at ~85°C and allowed the system to sit for 10 minutes to ensure thermal equilibrium. At this point, we removed the system from the oven, placed it in a vacuum chamber, and reduced the pressure inside the chamber to -25 inHg for 1-2 minutes. Once air bubbles stopped emerging from the molten metal bath, we removed the impregnated foam samples from the molten metal bath, laid them on a flat acrylic surface, and allowed them to cool to room temperature. We then removed the thin metal skin that remained on the surface of the sample and measured the weight of the composite. Given the silicone and Field’s metal densities and volume fractions, we could calculate the expected total mass of the composite—which we did—and compared that with the measured mass. If the measured mass was too low, we returned the composite sample to the molten metal bath, waited for thermal equilibrium, and repeated the vacuum process.

2.5.3 Tension Tests

All tension tests were uniaxial, performed on a Z010 Zwick Roell equipped with a

BW91272 thermal chamber at a strain rate of 0.36 min-1. This rate was chosen as a compromise

between the testing standards for rubber (ASTM D412 – 06a(2013)) and those for metal (ASTM

E8/E8M – 15a). All tensile samples were fabricated according to the dumbbell dimension standard

Die A in ASTM D412 – 06a(2013).

2.5.4 Compression Tests

All compression tests were uniaxial, performed on a Z010 Zwick Roell at a strain rate of

0.36 min-1. This rate was chosen to match that of the tension tests. All compression samples were fabricated according to the “short” cylinder dimension standard in ASTM E9-09.

2.5.5 Tension Tests of Empty Elastomer Foam and the Composite

These tests were conducted using the sample fabrication and testing method described in

“Tension Tests”. We tested 2 empty elastomer samples and 2 composite samples.

2.5.6 Tension Tests of Sealed Empty Elastomer Foam and Sealed Composite

We fabricated dumbbell samples for tension tests using the fabrication method described in “Tension Tests”. We then sealed those samples in a 3 mm skin of a lower elastic modulus silicone (Ecoflex® 0030, Smooth-On). We tested one empty elastomer sample at room temperature, one composite sample at room temperature, two empty elastomer samples at 80°C and four composite samples at 80°C. These tests were conducted to failure of the composite, before the skin ruptured. Each test at 80 °C was conducted within the thermal chamber after heating for

30 minutes to attain thermal equilibrium.

2.5.7 Tension Tests of Self-Healed, Welded, and Virgin Composite Samples

We fabricated dumbbell samples for these tests using the fabrication method described in

“Tension Tests”. To create self-healed samples, we cut the dumbbells at their vertical middle using a sharp razor blade. We then heated the samples to ~85°C, placed the two cut surfaces in contact,

and allowed the samples to cool back to room temperature. To fabricate welded samples, we cut three samples at their vertical middle and re-paired the segments so that no dumbbell half was paired with its original partner. We then heated the samples to ~85°C, placed the two cut surfaces in contact, and allowed the samples to cool back to room temperature. We tested three self-healed, three welded, and three virgin samples using the tensile testing method described above.

2.5.8 Compression Tests of Empty Elastomer Foam and Composite

These tests were conducted using the sample fabrication and testing method described in

“Compression Tests”. We tested four empty elastomer samples and four composite samples.

2.5.9 Repeated Welding Tests

Table 2.1 shows the results of an experiment conducted to demonstrate the strong capillary forces. Two independent composite pieces were welded and separated repeatedly and their masses measured at each step. The masses of the individual pieces changed by less than 0.7% at each step.

The small changes in mass could be due to handling error when pulling the samples apart.

2.5.10 Repeated Self-Healing Tests

Figure 2.8 shows that this material can self-heal at least 3 times with a slight decrease in elastic modulus each round. Tensile tests were conducted using the sample fabrication and testing method described in “Tension Tests of Self-Healed, Welded, and Virgin Composite Samples”.

Two virgin samples were tested and their average taken. One healed sample was tested and re- healed three times in total. The reduction of elastic modulus is possibly due to the elastomer skin delaminating from the composite surface and enabling molten metal to flow to that surface. Due to testing constraints (e.g., sample geometry and mechanical testing configuration), slight mechanical stimulation at the healing site was needed to promote flow of the molten metal.

Improved fabrication methods that directly bond the elastomer skin to composite should mitigate the issues of mechanical testing.

Figure 2.8 Mechanical data for repeated healed sample. Mechanical testing data for a virgin sample and for one sample being repeatedly damaged and healed.

CHAPTER 3

SOFT OPTOELECTRONIC SENSORY FOAMS WITH PROPRIOCEPTION*

3.1 Introduction

Since its inception, the field of Soft Robotics has advanced from one-degree-of-freedom contractile actuators with open-loop control (i.e., McKibben artificial muscles4,5) to active three- degree-of-freedom mechanisms6,22–24,30, devices with closed-loop control44,89,91, and high-force actuators61,122. Contemporary elastomeric machines can also have both exteroception and proprioception through embedded strain and pressure sensors51,53,55,56,123, enabling them to sense and respond to external forces39. As elastomeric machines continue to grow in complexity, and as roboticists push the boundary of soft robot functionality, more sophisticated sensing will become necessary.

For a soft robot to robustly interact with its environment, it must know its current shape in three dimensions. To know its own configuration, an inherently compliant system must be able to sense deformation—whether it is self-induced through actuation or externally inflicted. The most commonly used sensors in soft robots are either surface-mounted for pressure and touch detection55–57,124 or embedded along neutral bending axes to measure the global curvature of a robot limb44,50,60,125. These types of sensors are typically integrated to measure a specific type of deformation (e.g. pressure at a certain point, bending along a certain axis), which limits the information they can give about a robot’s configuration. To fully know a soft robot’s shape, we may need to fabricate sensors that can detect arbitrary deformations; however, it may suffice to

* Van Meerbeek, I. M., De Sa, C. M., Shepherd, R. F. (2018) Soft Optoelectronic Sensory Foams with Proprioception. Science Robotics. Reproduced with permission. 29

pattern high densities of the currently available sensors and either derive a complex analytical model or apply machine learning techniques. Such an approach has been used on sensor systems to fabricate devices such as a gesture recognition device, a pressure sensor, and a robotic skin69,97,126,127. In a step toward soft actuator proprioception, we present an elastomeric foam that can sense macroscopic deformation via embedded optical waveguides and the use of machine learning and statistical techniques to interpret transmitted light intensities.

In this paper, we present an elastomeric foam sensor system that we have trained to sense when it is being bent and twisted. To achieve this goal, we embedded an array of optical fiber terminals into the base layer of an elastomeric foam (Figure 3.1). The fibers served to illuminate the foam as well as to detect diffuse reflected light. We bent and twisted the foam to known angles and gathered the intensity of the diffuse reflected light leaving each fiber. To produce models that predict the foam’s deformation state from the internally reflected light, we applied machine learning (ML) techniques to the data (Figure 3.2, Video 3.1). We chose to employ machine learning instead of deriving a theoretical model, because doing the latter would have been very difficult given the large number of independent variables, many of which would have been difficult to accurately measure. Those independent variables include: foam porosity, foam geometry, strut geometry, optical fiber placement, optical fiber terminal orientation, refractive index of the silicone, loss of the optical fibers, and absorption of the silicone. Diffusing Wave Spectroscopy

(DWS) in cellular and colloidal substances has been used previously to gather information about microstructural statistics128; however, this technique does not yield macroscopic shape specificity and has not been applied to robotics. We combined this platform of DWS with machine learning to create a soft robotic sensor that can sense whether it is being bent, twisted, or both, and to what degree(s).

Figure 3.1 Foam assembly design. (A, left) Foam and optical fiber assembly in three stages of fabrication. (A, right) Cross section of foam and optical fiber assembly in three stages of fabrication. (B) Diagram of foam and optical fiber assembly.

To detect sensor deformation, we selected and evaluated two distinct approaches. The first approach used single-output classification to detect whether the sensor was being bent or twisted, followed by single-output regression to predict the magnitude. This approach allowed us to detect one deformation mode at a time. The second approach enabled us to detect bending and twisting

simultaneously by using multi-output regression. To model the foam’s state for the first approach, we defined two variables: Deformation Mode and Angle. Deformation Mode is a categorical variable that can hold one of four values: bend positive, bend negative, twist positive, or twist negative. Angle is a real-valued number corresponding to the magnitude of the bend or twist experienced by the foam. Using the values of Deformation Mode as training data labels, we trained a single-output categorical model to predict the type of deformation. Then, using the values of

Angle as training data labels, we trained four single-output regression models (one for each

Deformation Mode,) to predict the magnitude of the deformation after the deformation had been categorized. We compared three classifiers—k-Nearest-Neighbors (kNN), Support Vector

Machines (SVM), and Decision Trees—and six regression models—kNN, SVM, Decision Trees,

Gaussian Processes (GP), Linear Models, and Multilayer Perceptrons (MLP) (also known as

“Neural Networks”). The best classifiers had a test error rate of 0 and the best regression models had a test mean absolute error of 0.06 degrees. For the second, multi-output approach, we modeled the foam’s state as a 2-dimensional vector of real-valued numbers representing the bend and twist angles experienced by the foam. With this label format, we trained a multi-output regression model to predict the bend and twist angles simultaneously. We compared three multi-output regression models—kNN, Linear Models, and MLPs—and found that the best model had a test mean absolute error of 0.01 degrees.

3.2 Materials and Methods

3.2.1 Research objectives and design

Our objective is to demonstrate that elastomeric foam (and by extension, robotic elastomeric foam actuators) can be imparted with proprioception through optical sensing and the application of basic machine learning and statistical methods. To make the work accessible, we

chose a readily-available, soft-lithography process to fabricate the sensor system, and we implemented some of the simplest machine learning algorithms.

Figure 3.2 Sensor functionality. (A, B) Optical fiber terminals from which light intensity is read. (C-E) Real images of deformed foam and optical fiber assembly. (F-H) Real images of deformed foam and optical fiber assembly overlaid with computer reconstruction of the assembly's state.

3.2.2 Sensor design and fabrication

We wanted the sensor system to be easily integrated into a soft robotic actuator, therefore our sensor design is identical to that of our previously published soft foam actuators 24,65: we fabricated an open-cell, lost-salt silicone foam block which we embedded with optical fibers and sealed with a solid silicone skin. This fabrication technique can be used to create three-dimensional shapes, which makes this work generalizable to other soft mechanisms. We chose optical sensing because unlike its resistive and capacitive counterparts, it requires no embedded electronics, can sample a large volume with few probes, and is minimally affected by changes in temperature. For the embedded optics, we used plastic optical fibers with radius r~0.25 mm

(www.thefiberopticstore.com), which experience low loss (< 0.25 dB m-1 for 650 nm) and can be used to both illuminate as well as to detect light scattered in the foam. Plastic optical fibers can also be thermally shaped, which facilitates fiber terminal placement inside the foam. The input light came from a constant-output, visible light source (Edmund Optics, 115V, MI-150 Fiber Optic

Illuminator) to enable consistent results and facilitate troubleshooting respectively. For manufacturing simplicity, we used a camera (Edmund Optics, EO-13122C Color USB 3.0) to detect the diffuse reflected light exiting the fibers.

We used soft lithography to fabricate the sensor, which allowed us to pattern the optical fibers as a layer of the fabrication process. By selecting silicone rubber as the base material, the sensor can achieve high extensibility and experience little hysteresis. In addition, silicone comes in a large range of elastic moduli, enabling our design to generalize for a variety of applications.

We chose Smooth-On’s EcoflexTM 0030 specifically for its translucence and low tangent moduli, facilitating internal illumination and enabling large deformations for small forces, respectively.

We fabricated the optical foam assembly by first thermally forming optical fibers to form a planar array of fiber terminals, then casting and curing silicone rubber around those fibers (Figure 3.1A,

top). Next, we casted a mix of table salt and uncured silicone on top of the exposed fiber terminals, allowed the silicone to cure, then dissolved the salt out in water (Figure 3.1A, middle). In the last soft lithography step, we sealed the foam with solid silicone skin (Figure 3.1A, bottom). For reproducible training, we mounted one end of the optical foam into a bending and twisting apparatus and mounted the other end to a rigid post (Figure 3.2, Figure 3.3A). Using a 3D printed

(Objet30 Scholar, Stratasys, Inc.; VeroBlue material) connector and epoxy, the loose fiber terminals were directed into a chamber containing a beam splitter (Edmund Optics, 50R/50T Plate

Beam Splitter). We also pointed the illumination source and the camera into the beam splitter chamber in a configuration that separated the light entering the fibers from the reflected diffuse light exiting the fibers (Figure 3.3B).

Figure 3.3 Experimental setup. (A) Bird's-eye view of experimental setup. (B) Diagram illustrating how each fiber serves as illuminator and light detector via a beamsplitter.

3.2.3 Experimental design – model selection

One way to reconstruct the shape of a deformed elastomeric foam using the waveguide output intensities would be to derive a complete theoretical model of the system. To effectively achieve this goal, however, we would at minimum need accurate dynamic models of the complex interactions between features such as foam porosity, strut size, strut shape, refractive index, absorbance, reflectivity, input light wavelength, optical fiber position, and optical fiber orientation.

In the absence of a complete and accurate theoretical model, we used machine learning and statistical techniques to generate our models. We compared several machine learning models, all of which can be implemented using built-in software packages. We chose to use Matlab to facilitate transferring data from the camera to the prediction models, and to implement the different machine learning techniques, we used the following toolboxes: Statistics and Machine Learning

Toolbox, Curve Fitting Toolbox, and Deep Learning Toolbox.

Figure 3.4 Gathering data. (A, B) Real images of foam and optical fiber assembly during deformation, in darkness. (C) Schematic of training data collection process.

3.2.4 Experimental design – machine learning implementation

To gather data, we covered the optical setup (Figure 3.3) to avoid interference due to changes in ambient light. With the illuminator on, we deformed the foam to a known bend or twist angle, saved an image of the fiber terminals, calculated the average intensity of each fiber terminal, and saved those scalar values in a vector of length 30. For single-output prediction, we repeated this measurement 2,020 times for bend and twist angles in the range [-80,90] and [-82,90] respectively, resulting in a feature matrix, X, of dimension 2,020 × 30 and a label matrix, Y, of dimension 2,020 × 2 (Figure 3.4). The first column of Y held the values for Deformation Mode, and the second column held the values for Angle. We gathered 290 test data points in the same manner. For multi-output prediction, we repeated the above process to gather 956 training data points and 239 test points.

To train the categorical classifiers, we used the built-in Matlab functions fitcknn for kNN and fitcecoc for both SVM and the decision tree. To train the regression models, we grouped the training data by deformation mode, then generated four regression models, two for each deformation mode using the built-in Matlab functions knnsearch for kNN, fitrsvm for SVM, fitrtree for the decision tree, feedforwardnet and train for MLP, fitlm for the linear model, and fitrgp for GP. To train the multi-output models, we used knnsearch for kNN, feedforwardnet and train for MLP, and mvregress for Linear. For each model, we performed a random hyperparameter search to find the best model. Table 3.1 displays the best hyperparameter sets found by our search.

Single-output classification models Model Best model hyperparameters kNN NumNeighbors = 1 Distance = “euclidean” SVM KernelFunction = “gaussian” KernelScale = 32.2072 Tree MinLeafSize = 1 MaxNumSplits = 1322 SplitCriterion = “twoing” Single-output regression models BP BN TP TN Model Best model hyperparameters kNN NumNeighbors = 1 NumNeighbors = 1 NumNeighbors = 1 NumNeighbors = 2 Distance = “correlation” Distance = Distance = “cosine” Distance = “chebychev” “correlation” SVM KernelFunction = KernelFunction = KernelFunction = KernelFunction = “polynomial” “gaussian” “gaussian” “gaussian” KernelScale = 1 KernelScale = 9.0488 KernelScale = KernelScale = 4.2965 Order = 2 15.1503 Tree MinLeafSize = 2 MinLeafSize = 5 MinLeafSize = 1 MinLeafSize = 4 MaxNumSplits = 80 MaxNumSplits = 106 MaxNumSplits = 80 MaxNumSplits = 66 GP KernelFunction = KernelFunction = KernelFunction = KernelFunction = “RationalQuadratic” “RationalQuadratic” “RationalQuadratic” “RationalQuadratic” MLP HiddenLayers = 5 HiddenLayers = 4 HiddenLayers = 3 HiddenLayers = 4 Neurons = [35, 43, 36, Neurons = [20, 14, 13, Neurons = [8, 48, 6] Neurons = [33, 32, 16, 18, 5] 13] 12] Linear n/a n/a n/a n/a Multi-output regression models Model Best model hyperparameters kNN NumNeighbors = 4 Distance = “correlation” MLP HiddenLayers = 4 Neurons = [48, 44, 28, 39] Linear n/a

Table 3.1 Model parameters for best prediction models. Best hyperparameters found via random search.

3.3 Results

3.3.1 Model Performance on Test Data

We trained each single-output classifier on a training dataset of 2,020 observations. We evaluated their performance on a set of 290 unseen observations. In both datasets, the range of bend angles was [-80,90] and the range of twist angles was [-82,90]. These bounds represent the physical limits of our testing apparatus. Of the classifiers tried, the kNN and SVM models

performed best with a classification test error rate of zero. To predict the magnitude of the deformation mode, we partitioned the training dataset by deformation mode and trained one regression model for each partition (four total models). We repeated this process for each of the six regression models we wanted to compare. The kNN regression model had the lowest mean absolute error at 0.06 degrees Table 3.2 and Table 3.3 display the full results of these evaluations.

We qualitatively demonstrated one of the composite model’s performances by deforming the sensor in real-time and displaying a geometric reconstruction of the foam’s deformation state based on the model’s predictions (Video 3.1). The prediction models used for this demonstration were the kNN classifier and the GP regression model.

kNN SVM Tree 0 0 0.05 Table 3.2 Classifier model error rate. Error rates of the classification models.

kNN GP MLP SVM Tree Linear Bend Up 0.07 1.59 1.74 3.10 5.02 6.50 Bend Down 0.08 1.88 2.72 2.92 5.25 8.92 Twist CW 0 1.81 2.36 1.98 4.50 5.87 Twist CCW 0.07 2.05 2.39 3.27 4.43 5.92 Mean 0.06 1.83 2.30 2.82 4.80 6.80

Table 3.3 Single-output regression model errors. Mean absolute errors for each deformation mode. CW: Clockwise, CCW: Counterclockwise kNN MLP Linear 0.01 1.43 13.9 Table 3.4 Multi-output regression model errors. Mean absolute errors.

The multi-output regression models were trained on a dataset of 956 observations. To evaluate their performance, we gathered a test dataset of 239 observations, and of the models tried, kNN performed best again with a mean absolute error of 0.01 on the test dataset. Table 3.4 displays

the full results for these trials. In machine learning, model parameters are those whose values are set during training (i.e. learning). Some examples are the slope and intercept for a linear model or the hyperplane and margin size for SVM. A hyperparameter, by contrast, is a parameter whose value must be set before training. Hyperparameters help define the structure of the model being used. An example is the number of hidden layers in an MLP (i.e. neural net). For both the single- output and multi-output models that had hyperparameters, we optimized them using random search129. All reported values come from the best hyperparameter sets we found. Table 3.1 displays the hyperparameters we used for each model.

Figure 3.5 Results from k-fold cross-validation. Error bars represent standard deviation.

3.3.2 Cross-Validation

To assess how well our models would perform on new data, we performed non-exhaustive, k-fold cross-validation130. Cross validation is a method used to estimate model error on unobserved data by splitting the available data into subsets for training and subsets for evaluation. In k-fold cross-validation, the available data is randomly partitioned into k evenly sized subsets. Next, we reserve one subset for evaluation and train a model using the union of the remaining k-1 subsets.

We repeat this process for each subset—k times—such that k models are trained and evaluated.

The errors of the k models on their corresponding validation sets are estimates of the test error of a model trained on the entire dataset. The variance between the k models indicates how much model error varies with the training data. The results of the k-fold cross-validation are displayed in Figure 3.5. We found that the models had low error, indicating a likelihood of low test error.

Most of the models also had relatively little variance, suggesting that they did not depend heavily on the training data used. With this knowledge, we created our final models using all the gathered data as training data.

3.3.3 Training Data Size (n)

To determine how many training observations were required to obtain useful models, we took increasingly smaller subsets of the training data and generated new models based on those smaller training data sets. For single-output prediction, an exhaustive search of all possible training

,! data subsets would have required ∑,, = ∑, ≫ 10 trials for each !(,)! prediction model (three classifiers and six regression models). We did not have the computational capacity to do the exhaustive search, therefore for each model, we performed 300 trials for 19 different subset sizes each, for a total of 9 models × 300 trials × 19 subset sizes = 51,300 trials, which was the number of trials our machine could process in 10 hours (e.g. overnight). The MLP

trials took longer, therefore we only performed 15 trials for each subset size. We evaluated each trial’s model on the test dataset (290 data points). We performed a similar process for the multi- output prediction models.

As is typical, we found that as the number of training observations increased, model performance improved (Figure 3.6). The kNN classification error rate remained below 0.01 for models trained on datasets as small as 56% of the original training dataset size, and the single- output kNN regression mean absolute error remained below 1.0 degree for models trained on sets as small as 62% of the original training set size. The multi-output kNN regression mean absolute error also remained below 1.0 degree for training datasets as small as 75% of the original set. For most model types, the error appears to be approaching a plateau at the maximum training data size we used, suggesting that the performance of our largest training dataset may be slightly, but not greatly improved by collecting more data.

3.3.4 Feature Set Size (d)

To determine the relationship between model performance and optical fiber detector density, we removed randomly generated subsets of features (i.e. fiber intensity data) from the training and test data. We trained and evaluated new models using the modified training and test data. The complete, unmodified training data had a feature set of size d = 30 (for the 30 fibers). To exhaustively search all possible feature subsets, we would have needed to generate and test

! ∑ = ∑ ≈ 1.07×10 models for each of the models we compared. We did not !()! have the computational power for these many trials, therefore for each feature set size, we randomly selected a quantity of subsets equal to the smaller of 300 and the maximum number of possible subsets for that feature set size (d-choose-f where f was the size of the feature subset).

Again, we chose this number of trials based on a computation time of 10 hours, and the number of

MLPs tested for each feature set size was reduced to 11 due to its greater runtime.

Figure 3.6 Effect of training data size. Classification and regression performance on test data as a function of training data size. Each plot point represents the mean across random trials, and the error bars represent standard deviation across trials. Classification error is 0-1 loss.

Figure 3.7 displays the full results for this experiment. We found that the single-output kNN classification error remained below 0.1 for feature set sizes as small as 10, and the kNN regression model error remained below 1.0 degree for feature set sizes as small as 12 fibers. The multi-output 43

kNN regression error remained below 1.0 degree for models with as few as nine fibers (i.e., features). These results suggest that our system could be redesigned to have as little as a third the reported fiber density, which could be useful when designing a full soft robot embedded with this sensing system.

To determine whether certain fibers affected model performance more than others, we conducted another experiment where we removed fibers, then trained and tested new models. For this experiment, however, instead of randomly removing subsets of fibers, we searched for the fiber which, when removed, produced a model with the highest test error and removed it from the data. We repeated this process until four fibers remained. Figure 3.8 shows these results plotted with the results from the randomly removed feature subsets for each model. We found that greedily removing fibers from the data produced slightly better models than randomly removing fibers, suggesting that some fibers do affect error slightly more than others.

3.4 Discussion

In general, machine learning model error can have three main causes: (1) the training data may not fully represent the unobserved data; (2) the data may be noisy; and (3) the model assumptions may be incorrect (e.g. assuming that the data is linear when it is not). The cross- validation results displayed in Figure 3.5 show that our models had relatively low variance, indicating that the training data may represent the full space well. The mean signal-to-noise ratio of all fibers (signal mean divided by the standard deviation of the noise) is 185, and when we propagated the signal noise through our models, we found little to no change in model prediction.

Given the low cross-validation variance and limited effect of noise on prediction, the main contributor to model error in our experiments may be incorrect model assumptions (i.e. model bias). If model bias is the main contributor to prediction error, then k-Nearest-Neighbors’ lower

average error across all trials may be due it having the best model assumption of the models we compared (i.e. similar inputs have similar outputs). Also, kNN has been shown to have low model bias. Cover and Hart showed that as the training data size approaches infinity, for k = 1, kNN error is no more than twice the error of the best possible classifier131.

Figure 3.7 Effect of feature set size. Classification and regression performance on test data as a function of feature set size. Each plot point represents the mean across random trials, and the error bars represent standard deviation across trials.

Figure 3.8 Random vs. greedy feature removal. “Rand. mean” represents the mean error for the models generated with randomly removed features. “Rand. min.” represents the minimum error found with the same randomly removed features. All errors are test errors. Classification error rate is 0-1 loss, and regression error is mean absolute error.

kNN’s lower error may make it the most effective model for this application; however, there are other factors to consider. The cross-validation results show that some models had lower variance than others. Specifically, the kNN, GP, and SVM test errors varied little between training data sets, while the MLP and Tree models in particular showed much more variation. If the training data is limited for some reason, one may want to pick the models with lower variance. One may also consider evaluation time. Table 3.5 shows the mean time to evaluate one observation for each model. Although kNN models can often have slow evaluation times when the training set is large, since the training sets in this research remained small, the evaluation times were the same order of magnitude as most of the other models. Given that kNN showed desirable traits regarding error, variance, and evaluation speed, it stands out as one of the most useful models in this application.

For a robotics system that makes decisions based partly on prediction confidences; however, the

GP model could be the most useful, since it outputs predictions as well as confidence values for each prediction.

Several studies examining human proprioceptive capability through limb-matching tasks have found that wrist, finger, and elbow joint angle absolute errors lie between 1 and 12 degrees

132–136. In particular, proprioception of the proximal interphalangeal joint angle has an absolute error between 4 degrees and 9 degrees136. These results suggest that this level of error in proprioception is acceptable for tasks such as writing and reaching for objects. Given that the human index finger is on average 82 mm in length137,138, and that our sensor is 80 mm in length, we can loosely compare the performance of our sensor to that of the proximal interphalangeal joint on the human index finger. Scientists have shown that the proximal interphalangeal joint is located at about the midpoint of the finger138, therefore a joint angle error of 4 to 9 degrees corresponds to a fingertip position error of 3 to 6 mm. Given the geometry of our sensor’s measured bending angle

(Figure 3.3), the mean bend error obtained by, for example, the GP models (1.74 degrees) corresponds to an error of about 2 mm in the position of the sensor’s movable end. The kNN regression model has a smaller bend error, which corresponds to an even greater accuracy. With this comparison, we believe that our foam sensor system has the potential to greatly improve soft robotic control.

Single-output classification models Model Mean evaluation time (milliseconds) kNN 1.7 SVM 2.9 Tree 3.5 Single-output regression models Model Mean evaluation time (milliseconds) kNN 0.75 SVM 0.29 Tree 0.20 GPR 0.55 Linear 0.0018 MLP 8.3 Multi-output regression models Model Mean evaluation time (milliseconds) kNN 0.17 Linear 0. 0024 MLP 9.7

Table 3.5 Model evaluation times. Mean evaluation time of each model on one test data point.

To apply this system to a soft robot, one would need to design the integration of optical fibers into the soft actuators. They would also need to integrate the illumination and detection devices. We used a large illuminator and a camera; however, the illuminator could be replaced with LEDs, and the camera could be replaced with photodiodes. The beamsplitter setup could be miniaturized, or it could be removed, and the number of embedded fibers doubled. We chose not to do these integrations because we wanted to keep the system fabrication simple and highlight the

performance of the prediction models rather than the engineering challenges. To remove ambient light interference, an optically opaque elastomer skin would also need be used. We did not do this here to facilitate troubleshooting. Lastly, one would need to design a mount for the robot in order to gather accurate data for the machine learning models.

Our current system detects four deformation modes; however, we believe that other deformation modes could be added as needed. We also suspect that, with more sophisticated machine learning techniques, the sensor system could detect deformations that were not predetermined by the experimenters. Further research will investigate this possibility in order to achieve arbitrary deformation detection in soft robots.

We have seen in biology139–141 and in engineering142,143 that more complete and accurate sensing enables better control. This work is a step toward making soft robots more reliably controllable and more responsive to their environment. With this kind of sensing capability, soft robots could protect themselves by responding to excessive deformation. Walking soft robots could improve their locomotion by learning better walking gaits through proprioception. In addition, they could relearn to walk after experiencing limb damage.

To the best of our knowledge, this is the first optical robotic device that can sense multiple deformation types without sensors that have been specifically patterned for each type. While we present deformation classification that is limited to four modes (i.e. bend positive, bend negative, twist positive, and twist negative), we hypothesize that this method could be used for many deformation types. We also believe that classifying arbitrary deformation may be possible with more sophisticated machine learning techniques.

CHAPTER 4

COMPARING HYPERPARAMETER OPTIMIZATION TECHNIQUES FOR DATA

AUGMENTATION TO FIX SENSOR DRIFT IN A SOFT ROBOTIC SENSOR*

4.1 Introduction

In recent years, rubber-based robotic devices have improved in complexity, force output, manufacturing capability, and sensing. The field began with one-degree-of-freedom bending actuators and today has realized three-dimensional shapes that can actuate in all three dimensions22–24,30. Force output has improved due to more sophisticated manufacturing techniques61,122. Researchers have developed soft strain and pressure sensors51,53,55,123, some of which have been embedded into soft devices, enabling them to sense and respond to external forces39,56. The field has also seen advances in control due to these capabilities44.

As soft robotic devices become more complex, more sophisticated sensing will prove necessary. For a soft robot to successfully interact with the environment, it must know its own configuration, for which it needs to sense its deformation—whether that deformation is self- induced through actuation, or externally inflicted. Currently, the most commonly used sensors in soft robots have been surface sensors that sense pressure and touch55–57 and structural strain sensors39,50,60,125. Sensors have also been developed that can detect externally-inflicted deformation87 and gestures144, but these sensors are not easily integrated into a robotic device with the potential to manipulate its environment.

We have developed a sensor system comprising 30 constitutive sensors that, using k-

* Van Meerbeek, I. M., De Sa, C. M., Shepherd, R. F. (2019) Addressing Sensor Drift in a Proprioceptive Optical Foam System. SPIE Smart Structures and NDE, Abstract Accepted 50

Nearest-Neighbors (kNN) and linear regression (LR), detects different types of macroscopic deformation (e.g. ‘twist’, 25°). However, the trained models only work well for a short period of time after training. As the sensor system experiences more deformation, the constitutive sensor values drift (Figure 4.1), resulting in unusably large regression error. This phenomenon may be considered “concept drift”145. To combat this, we employed data augmentation. We augmented the training data set by duplicating all observations and adding the same vector of offset values to each duplicate observation. For our first attempt, we calculated the difference in the mean fiber values for the training dataset and the new, drifted dataset. When we applied this mean offset value to the training dataset and generated new prediction models, the classification error did not improve. This lack of improvement may be due to the model we used (kNN). A different classification model may be necessary to be able to address sensor drift in this way. However, the regression validation error was reduced from 22.9 degrees to 14.1 degrees. This value was still more than double the original linear regression test error of 6.8 degrees, so in this work, we conducted several searches to find offset values that would result in a greater decrease in regression error. Doing an exhaustive search for the optimal 1×30 vector requires searching through k30 possible augmentation parameter sets where k is the number of considered values. Even when k equals 2, this problem becomes intractable; therefore, we compare three well-known hyperparameter optimization techniques: grid search, random search129, and Bayesian optimization146.

4.2 Related Work

This project has two main components: 1) utilizing data augmentation to solve issues of sensor drift and 2) using automated hyperparameter optimization to find the best augmented models.

Researchers have implemented machine learning techniques to solve sensor drift issues

before. Vergara et al.147 used a combination of prolonged data collection and an ensemble of classifiers (based on support vector machines) to handle drift in chemical sensors. Kaneko et al.148 used online support vector regression to solve “soft” or “virtual” sensor drift. Nguyen et al.149 combined data augmentation and a support vector machine to handle what they call “label-drift”

(handling never-been-seen labels online) in large-scale data set models.

Figure 4.1 Sensor Drift. Intensity data for some of the fibers while the sensor system was being twisted. The red and blue data sets were taken about one week apart. Angles are in degrees.

Although several papers have used support vector machines to combat concept drift, we use data augmentation for two reasons: 1) This particular scheme seemed like an intuitive way to mimic what the sensors were doing. 2) We could not find others who have already tried this.

Automated hyperparameter optimization has also become a popular research topic in the past years. Bergstra et al.129 showed that random search is more efficient than grid or manual

search; Snoek et al.146 developed a framework for using Bayesian optimization to optimize hyperparameters; and MacLaurin150 developed a gradient-based hyperparameter optimization method. In this work, we implement the methods described by Bergstra et al.129 and Snoek et al.146.

4.3 Experiments

To gather the original training data, Xtr, we deformed the sensor system to known angles of twist and bending and recorded the 30 constitutive sensor values. We divided the training data into the four categories: twist left, twist right, bend up, bend down, and trained separate linear models for each category. We therefore had to perform four separate augmentations for each model. We used the following steps to generate the augmented data sets:

Algorithm 1 Augmentation Scheme n×30 requires: Xtr ∈ ℝ , n = number of observations normalize rows of Xtr offsets ∈ ℝ1×30 offsets_repeated ∈ ℝn×30

Xtr_augmented = Xtr ∪ (Xtr+offsets_repeated)

The offset values were chosen randomly from within the range [-0.1, 0.1].

4.3.1 Grid Search vs. Random Search

For both grid search and random search, we generated a list of 1.05e6 offset vectors, which we then looped through and tested. (This took around 3.75 hours for each deformation type.) Due to the large number of hyperparameters, the grid search offsets were limited to two values: -0.05 and 0.05. Each random offset value was selected randomly from [-0.1, 0.1]. The models with the lowest mean absolute error were saved. We expected random search to find better models more quickly than grid search.

4.3.2 Grid & Random Search vs. Bayesian Optimization

To implement Bayesian Optimization, we used the built-in MATLAB function called bayesopt. We set the maximum time to be 3.75 hours for each deformation type, so that it would be consistent with the grid and random search experiments. We performed three Bayesian optimizations: one with the activation function “expected improvement”, one with “expected improvement per second”, and one with “probability of improvement”. Based on the findings by

Snoek et al.146, we expected to see that the Bayesian optimizations would find better models more quickly than random search and that “expected improvement per second” would be the most efficient acquisition function.

4.3.3 Test Data

To test our optimized models on unobserved data, we collected 50 data points for each deformation mode and predicted the test data's bend and twist values using the augmented models that had improved validation error.

4.3.4 Data Augmentation vs. Data Shifting

In addition to generating new models by augmenting the original training datasets, we trained new models by first shifting the training datasets. For these experiments, we calculated the mean offsets between the original training datasets and the drifted datasets, then added these offset values to the original training data points. We initially reserved a fraction of the drifted data to use as test data.

4.3.5 Data Modification vs. Training a New Model with New Data

To determine whether data augmentation or data shifting would be more or less effective than simply retraining a model on the new, drifted data, we took increasingly large subsets of the drifted data and for each subset, we trained three new models: one using the drifted data subset as

the training data, one using an augmented version of the original training dataset that was augmented using the mean offset between the original training data and the drifted data, and one using a shifted version of the original training dataset that was shifted using the mean offset between the original training data and the drifted data. We initially reserved a fraction of the drifted data to use as test data.

4.4 Results

Bend Up Bend Down Twist Positive Twist Negative Original 13.1 27.2 12.8 34.7 Grid Search 8.5 15.6 10.0 15.3 Random Search 7.6 11.9 10.0 12.9 Bayesian Opt. 1 7.9 13.1 10.9 15.5 Bayesian Opt. 2 8.5 14.0 11.0 14.8 Bayesian Opt. 3 8.3 12.6 10.8 14.3

Table 4.1 Validation Errors for Best Models. (in degrees)

4.4.1 Grid Search vs. Random Search

Figure 4.2 shows the results from the grid and random searches. Both optimizations used the same code, therefore both took the same amount of time to attempt the same number of trials.

As expected, random search found higher accuracy models in fewer iterations/less time than grid search. The average error before augmentation was 22.0 degrees, and after augmentation using random search, was 10.6 degrees (for grid search, it was 12.4). See Table 4.1 and Table 4.3 for more detailed error values.

4.4.2 Random Search vs. Bayesian Optimization

Figure 4.2 shows that although the Bayesian methods found better hyperparameters per iteration than random search, each iteration took longer. Random search was able to try many more points (over 1e6) in the same amount of time that Bayesian optimization performed 600 trials, which enabled it to outperform the Bayesian methods.

Figure 4.3 shows that the trials attempted by random search produce many models with increased error rather than decreased, while Bayesian optimization trials produced mostly models that have similar or decreased error.

4.4.3 Bayesian Optimization Acquisition Functions

We performed Bayesian Optimization with three different acquisition functions: “expected improvement”, “expected improvement per second”, and “probability of improvement”.

According to Snoek et al.146, “expected improvement per second” should have performed best, but in our experiments, it was the least successful, and “probability of improvement” found the models with the lowest error.

Figure 4.2 Grid Search vs. Random Search vs. Bayesian Optimization. Errors are validation errors. Mean absolute errors are in degrees. ‘Bayes1’ used expected improvement for the acquisition function, ‘Bayes2’ used expected improvement per second, and ‘Bayes3’ used

probability of improvement. While random search completed over 1e6 iterations in 3.75 hours, the Bayesian optimizations only got through about 600 iterations in 3.75 hours, therefore the left plot ends at 600 iterations for all optimizations for readability.

Figure 4.3 Random Search vs. Bayesian Optimization. Mean absolute error in degrees.

4.4.4 Test Data

Table 4.2 shows the test error of the best models found during augmentation. (These models are the same as those whose results are displayed in Table 4.1.) We can see that the models found using random search are no longer the best performers when used for new, test data. We also see that in the augmentation of the model for deformation mode “twist positive”, all the augmented models perform worse than the original model. However, in general, most of the augmented models do improve performance, confirming that this method can be used to decrease error due to sensor drift.

Table 4.3 combines the models for all four deformation types and compares their overall mean validation error to their corresponding mean test error.

Bend Up Bend Down Twist Positive Twist Negative Original 18.5 23.7 15.5 43.2 Grid Search 15.3 11.4 17.5 24.2 Random Search 14.7 16.2 19.0 20.4 Bayesian Opt. 1 16.8 15.2 22.0 21.0 Bayesian Opt. 2 15.6 12.0 18.3 19.7 Bayesian Opt. 3 14.6 9.8 18.7 20.3 Table 4.2 Test Errors for Best Augmented Models. (in degrees)

Validation Error Test Error Mean Δ % Δ Mean Δ % Δ Original 22.0 25.2 Grid Search 12.4 -9.6 -43.7 17.1 -8.1 -32.1 Random Search 10.6 -11.4 -51.7 17.6 -7.6 -30.2 Bayesian Opt. 1 11.9 -10.1 -46.0 18.8 -6.4 -25.4 Bayesian Opt. 2 12.1 -9.9 -45.0 16.4 -8.8 -34.9 Bayesian Opt. 3 11.5 -10.5 -47.6 15.9 -9.3 -36.9 Table 4.3 Validation Error vs. Test Error.

Figure 4.4 Augmented Model Performance on Test Data. Mean absolute error in degrees.

4.4.5 Data Augmentation vs. Data Shifting

Table 4.4 displays the results from these experiments. We found that for both the kNN classifier and the linear regression model, the error on the unobserved dataset very close for both data augmentation and data shifting. In both cases, the models trained on augmented data had slightly lower error than the models trained on the shifted dataset.

Original After Augmentation After Shifting kNN Classification Error 0.49 0.46 0.48 Rate Linear Regression Mean 20.7 13.6 14.2 Absolute Error (degrees) Table 4.4 Data Augmentation vs. Data Shifting.

4.4.6 Data Modification vs. Training a New Model with New Data

Figure 4.5 shows the results from these experiments. We found that when the drifted data subset had less than about 200 observations, the modified data models performed better by having lower test errors as well as less variation in error as the subset size changed. The test error of the models trained on the drifted data (the black, solid line) increased dramatically around 150 observations before becoming monotonically decreasing and outperforming the models trained on the augmented data.

Figure 4.5 Training a New Model on Modified Data vs. New Data. Mean absolute error in degrees. Blue lines represent errors of the models trained on subsets of the shifted dataset. Red lines represent errors for models trained on subsets of the augmented dataset. Black lines represent errors from models trained on subsets of the drifted data. Dashed lines represent error of models evaluated on the dataset used as (black) or to modify (red and blue) the training dataset. Solid lines represent error on unobserved datapoints.

4.5 Discussion

We encountered a few surprising results in our experiments, particularly pertaining to random search and Bayesian Optimization.

4.5.1 Grid Search vs. Random Search

We hypothesized that random search would find models with lower error than grid search, and our experiments support this. We believe that this is mostly due to the large space being explored. It is impossible to search the entire space, so grid search will never reach certain regions of the parameter space. Random search, on the other hand, can search every general region of the space, allowing the possibility for it to get closer to the optimal solution.

4.5.2 Random Search vs. Bayesian Optimization

We hypothesized that Bayesian optimization would find better models than random search, but our experiments did not support this. Given more computation time, it is possible that Bayesian optimization would have found the best models, but as computation time is an important factor in optimization, random search performed most desirably in our experiments. Snoek et al.146 compare their Bayesian methods to “random grid search” and find that their Bayesian method outperforms it. They do not describe the “random grid search” method used, so it is difficult to say if this is more similar to random search or grid search. Eggensperger151 also claim that Bayesian methods outperform random search but provide no reference. Wang et al.152 show some results where random search and Bayesian optimization perform similarly, suggesting that Bayesian optimization does not always outperform random search. Given that we used the built-in

MATLAB Bayesian optimization function, it is difficult for us to speculate as to why it did not work as well as our random search algorithm. We would need to conduct more experiments with custom code.

4.5.3 Bayesian Optimization Acquisition Functions

We hypothesized that using the acquisition function “expected improvement per second” would produce the models with the lowest error; however, we found the opposite to be true.

“Probability of improvement” worked best, and “expected improvement per second” performed the worst.

In the work by Snoek et al.146, they choose “expected improvement” because they claim that it has been shown to be “better behaved” than “probability of improvement”; however, they do not explain why or refer to a previous publication showing this. Given our results, we speculate that “probability of improvement” may work best given the right conditions but may work less well in general than “expected improvement”.

It was also surprising that “expected improvement per second” performed worse than

“expected improvement”. Again, since we used the built-in MATLAB Bayesian optimization function, it is difficult for us to speculate as to why it did not work as well as expected. A closer look at this built-in function or building our own function would be required to analyze this result.

4.5.4 Test Data

The test results show that data augmentation does work to decrease the mean absolute error as sensor values drift. However, the error values are still a bit high to enable reliable, high resolution control. For some applications, this amount of error may be acceptable.

4.5.5 Data Augmentation vs. Data Shifting

On average, data augmentation outperformed data shifting very slightly for the linear models. We suspect that shifting the data rather than augmenting it resulted in some loss of information.

4.5.6 Data Modification vs. Training a New Model with New Data

These results suggest that data augmentation may be useful when there are under 200 new observations, but that when it is possible to gather more than 200 new observations, training a new

model on those observations alone may result in lower regression error.

4.6 Future Work

We anticipate continuing this work by building a robotic system that can perform tasks using these sensors. The sensor design is nearly identical to many rubber-based actuator designs, therefore its integration into a robotic part will be natural.

To improve the error further, it may suffice to run the hyperparameter optimization for longer; however, if that does not work, a new approach may be necessary. We may need to implement an online learning scheme similar to what Nguyen149 or Kaneko148 did.

4.7 Conclusion

In this work, we present an approach for handling sensor drift in a specific soft-material sensor system. As more soft robotic systems get developed, we may see an increase in the prevalence of sensor drift due to inherent compliance. This paper is a first attempt to solve this issue. To capture the state of soft systems, we may always need many sensors, therefore, optimizing our models containing several sensor values may always be a difficult problem. We compare three different hyperparameter search techniques: grid search, random search, and

Bayesian optimization and find that random search and Bayesian optimization produce improved models with similar error. This is promising for future work in this area.

CHAPTER 5

CONCLUSIONS

5.1 Summary of Contributions and Future Work

The field of soft robotics has made great strides in recent years, thanks to new fabrication techniques, novel sensor development, and improvements in material properties. For soft robots to become machines that industries rely upon, however, advancements still need to occur in soft hardware, sensing, and the interpretation of the sensory information. This dissertation presents advancements in each of these areas. Those advancements are summarized below.

A Metal-Elastomer Composite with Thermally Tunable Stiffness: In Chapter 2, I present a composite material of two interpenetrating foams—one of metal, the other, elastomer. This composite can change from a rigid, load-supporting material into a stretchable, low elastic modulus material through the application of heat. Tensile testing found that the elastomeric regime of the materials had an elastic modulus of 0.1 MPa, while the rigid regime had an elastic modulus of 1.8

MPa. I also demonstrate its ability to hold different shapes, actuate through shape memory, self- heal, and form larger structures through welding.

I embedded the metal-elastomer composite in a morphing wing-like pneumatic actuator to demonstrate the utility of its two stiffness regimes. Although the composite increased the stiffness of the wing while it was not actuated, after the composite was heated, the wing actuated with compressed air, and the composite cooled, the metal-elastomer was not tough enough to support the wing’s actuated shape after depressurizing the actuator. Since I fabricated the silicone foam using a loss-salt method, and the metal filled the voids left by the salt, the contact area between

metal grains was very small. I believe this factor is the largest reason for the low toughness of the material, and therefore its limited use as-is. However, elastomer 3D printing has become a reliable process, allowing new foam geometries to be much more easily explored. By fabricating different elastomer lattice structures and infiltrating them with metal, new versions of this metal-elastomer composite can be fabricated that have much better metal connectivity and therefore mechanical properties. With improved properties such as elastic modulus and toughness, this composite could be embedded in new or existing soft robotic devices for on-demand skeletons and therefore increased functionality.

A Soft, Optical Foam with Proprioception: Chapter 3 describes a foam embedded with optical fibers that can detect pre-defined deformation types through the application of machine learning. I present several types of models that fall into two main categories. The first category can be described as single-output or single-target prediction. These models used a two-step prediction process that first employed categorical models to predict the type of deformation experienced by the foam, and then used a single-output regression model to predict the angle of that deformation. The second category of predictions used multi-target or multi-output regression to predict the deformation state of the foam. The main advantage of this second approach is the ability to detect bending and twisting simultaneously. The best models predicted deformation magnitude with a mean absolute error of 0.06 degrees.

I specifically present the detection of bending, twisting, and both modes simultaneously; however, I hypothesize that with a more complex measurement apparatus that can deform a device in more than two ways at once, this optical device can be trained to detect several deformation modes. To be able to detect arbitrary deformation of a continuously deformable optical foam, it may suffice to use the multi-output prediction approach for detecting several deformation types

such as bending, twisting, shear, poking, and pinching; however, a new model of the foam may be required. One possible solution may be to use a 3D scanner to generate 3D models (e.g. STL files) of the foam in different deformation states while simultaneously reading the light intensities exiting the optical fibers. A multi-layer perception (i.e. “neural net”) might be an appropriate model to use for such an approach. Chapter 4 presents work toward reducing the model error due to sensor drift in the proprioceptive optical foam presented in chapter 3. By using data augmentation, the model test error was reduced from 25 to 17 degrees. A more effective approach may be to train a model that learns the sensor offset values, which could then be used to update the existing model rather than creating a new model with augmented data.

Many animals change their shape (or visual appearance) to communicate with or trick each other (e.g. the peacock and cuttlefish). With arbitrary deformation detection, a soft robot could controllably change its shape as a communication tool. Sea cucumbers stiffen their bodies in response to potentially dangerous stimuli such as excessive poking. With stiffness control, a soft robot could respond similarly when it detects a potential puncture. With improvement, the work in this dissertation could be applied to soft robots to make them as responsive to their environment and as adaptable as some living organisms.

APPENDIX A

POROELASTIC FOAMS FOR SIMPLE FABRICATION OF COMPLEX SOFT ROBOTS*

A.1 Introduction

The field of soft robotics uses compliant structures to reduce machine complexity and approach the mechanical18,61 and sensing58 capabilities of biology. Recently, soft (i.e., compliant and extensible) materials and structures have enabled machines capable of elaborate locomotion18,19,153 as well as analogs for caterpillars,27 fish,33,154 jellyfish,155 and octopus tentacles.23 These compliant machines often perform favorably when compared with conventional, rigid machines as they reduce control complexity,23 enable natural motion through continuous deformation,30 and interact gently with fragile objects.156

Fluidic Elastomer Actuators (FEAs) are a class of compliant machines capable of producing large deformations via pressurization of internal bladders.3 They operate similar to

McKibben artificial muscles157,158 though often require lower pneumatic pressures159. When internally pressurized, FEAs (typically composed of low elastic modulus silicone rubber) can bend,160 extend,161 or twist162 based on the specific patterning of inextensible fibers within the structure. During inflation, the inextensible fibers create a strain gradient resulting in the programmed motion. Although these machines exhibit complex motions with relatively few actuators,163 their fabrication has been largely limited to prismatic structures, which require complex assemblies to approximate the shapes and motions of biological models.159 Furthermore, these actuators require internal, connecting air chambers that often necessitate complex, costly,

* Mac Murray, B. C. et al. Poroelastic Foams for Simple Fabrication of Complex Soft Robots. Adv. Mater. 27, 6333 (2015). Reproduced with permission.

and time-consuming mold fabrication. Recently, foam-wax composites have been used to create soft, smart 3D structures that transcend prismatic designs,83 however these porous materials have not yet been used for fluidic actuation.

In this communication, we present a method to easily produce stochastic, open-celled, low density (ρ ~ 0.47 g ml-1) foams that when hermetically sealed form compliant actuators. Upon internal pressurization, these actuators are capable of large amplitude shape morphing while applying forces that exceed 20 N. Similar to cardiac muscle systems, where the soft tissue defines the function and shape of the organ (e.g. the heart), the poroelastic material forms the entirety of the machine. Unlike other FEAs, these machines have an interconnected open-pore network and require no additional molded air channels. Using existing forming techniques (e.g., casting, sculpting, and sheet cutting) we fabricated machines capable of actuating in simple modes such as bending and extension, as well as complex modes for functional devices such as suction cups and fluid pumps (Figure A.1a-c).

Figure A.1 Foam-based pneumatic actuation. (a) Bending actuator fabrication process (from left to right): curing porogen & PDMS mixture, heating to remove porogen, and patterning inextensible fiber into PDMS sealing layer, (b) bending actuation, (c) extending actuation, and (d) µCT foam reconstruction.

Our fluid powered foam actuators are significant because they allow simple production of complex soft machines that cannot easily be formed by other established methods. Though sacrificial 3D printed molds33 or manual assembly of prismatic structures164 can, with extra material and labor costs, produce 3D machines—these designs do not intrinsically link the robot’s body with its motion. As our fluidic actuators comprise the entirety of the machine, everywhere there is foam there is also the potential for motion. To demonstrate the potential of the poroelastic foam machines, we fabricated a soft, fluid pump with a complicated internal and external architecture. The pump we report is shaped like an organ, a human heart, and pushes fluid via pulsatile pressurization of two chambers. It is capable of pumping at flow rates (ν ~ 500 ml min-1) faster than any previous soft pump reported165–167 and at physiologically relevant pressures (ΔP ~

14 kPa).

A.2 Materials & Methods

We fabricated the foams via a lost-salt process adapted from Lin168 using silicone elastomer

(polydimethylsiloxane, PDMS) as the matrix material and ammonium hydrogen carbonate

(NH5CO3) as the fugitive porogen. An X-ray micro-computed tomography (µCT) reconstruction

(Figure A.1d) shows the full foam structure after salt removal. NH5CO3 is beneficial as a porogen because it (i) thermally decomposes readily and entirely above 50 °C, (ii) yields easily-managed

products (water, CO2, and NH3) leaving the PDMS foam residue free, and (iii) is inexpensive and readily available. We further describe the porogen thermal decomposition in the supporting information (SI) text.

We selected Mold Max 10 PDMS (MM10; Smooth-On, Inc.) as the elastomer due to its

low tensile modulus (E ~ 500 kPa) and large ultimate strain (휀 = >3), where 퐿 is the stretched length at break and 퐿 is the initial length, which enables large deformations at low

inflation pressures (typically ΔP < 70 kPa). Additionally, MM10 is beneficial as it exhibits a short

room temperature cure (~ 3 hr) and is compatible with the NH5CO3 porogen since it cures via an organotin-catalyzed condensation reaction. We note that the porogen will significantly inhibit the platinum catalyst in addition-cured PDMS resins.169 Though we selected a low modulus PDMS for this work, our process is general to all material systems compatible with the porogen.

To produce actuators, we sealed the foam structure in a ~2 mm thick layer of MM10 which we either brushed onto or molded around the foam. We preferred the brushing method when sealing irregularly shaped foams. Prior to curing the sealing layer, we patterned an inextensible, yet flexible nylon mesh (9318T18, McMaster Carr) to program the actuator motion upon inflation.

Though other fiber materials could serve the same function, we selected nylon mesh because it is easily laser-cut into complex shapes and creates an interwoven mechanical bond with the PDMS.

To characterize the mechanical properties of the foam, we performed uniaxial tensile tests on samples of ϕ = 0, 0.5, 0.6, and 0.7 porosity (i.e. pore volume fraction) and measured the forces applied by the sealed actuators via blocked force measurements. Additionally, we characterized the airflow rate through unsealed foam samples, since this parameter dictates actuation speed. We measured the input and output pressures (3847K71, McMaster Carr) across a foam disc (radius, r

= 1.25 cm and thickness, d = 1.25 cm) while measuring the air flow rate (FLDA3422G, Omega) through the system.

Figure A.2 Tensile and blocked force measurements. (a) Tensile stress-strain behavior of unsealed foams, (b) blocked force test setup, and (c) blocked force measurements of bending actuators composed of differing porosity.

A.3 Results & Discussion

Tensile tests on the unsealed foams show a trend of decreasing elastic modulus as porosity increases (Figure A.2a). The average tensile moduli, measured at ε = 1, of the ϕ = 0, 0.5, 0.6, and

0.7 porous foams were E ~ 508 kPa ± 28, 200 kPa ± 31, 83 kPa ± 6, and 48 kPa ± 19, respectively.

The average ultimate tensile stresses and strains were σUTS ~ 2.22 MPa ± 0.09, 0.40 MPa ± 0.02,

0.24 MPa ± 0.02, and 0.064 MPa ± 0.04 and εult ~ 3.56 ± 0.22, 1.97 ± 0.10, 2.35 ± 0.09, and 1.58

± 0.16 for the ϕ = 0, 0.5, 0.6, and 0.7 porous foams, respectively. The low variation within these samples (n=3 for each porosity tested) indicates good repeatability even though the foams are stochastically structured. The data also shows that all foams can stretch to ε >> 2 before failure; this elongation is essential to obtain large actuation amplitudes. Within the data, we also note that the pure (ϕ = 0) PDMS has a higher ultimate strain, 휀 ~ 3.3, than the foam materials. Due to this difference, the first component to fail during actuator over-inflation is the foam interior and not the encapsulating skin. Fortunately, for a pneumatic actuator in service, this failure mode is preferred over rupture of the external seal. The resulting expansion from foam fracture provides a visual indication of failure (we call it an “aneurysm”).

To characterize the performance of the actuators, we performed blocked force measurements on ϕ = 0.6 and ϕ = 0.7 porous samples. This measurement constrains bending actuators to a specific curvature (Figure A.2b) and measures applied force as a function of inflation pressure (Figure A.2c). Due to its lower modulus, the ϕ = 0.7 porous foam actuates at lower pressures; however, it also develops an aneurysm at ΔP ~ 50 kPa. The ϕ = 0.6 porous actuator inflates to higher pressures (ΔP ~ 80 kPa) without developing an aneurysm, and therefore applies a larger force. The relationship between inflation pressure and actuating force extends to ϕ = 0.5 porous foams (SI text); however, there was large sample to sample variation likely due to approaching a percolation threshold of pneumatic connectivity. The ability to tailor the onset and 71

magnitude of actuating force by porosity is a new capability for FEAs. We used the same blocked force technique to measure the force applied from an extending actuator and recorded an applied force of 20 N for ϕ = 0.7 porosity (SI Text).

To record airflow measurements through the foam, we used a custom-built acrylic cell to bond a cylindrical foam sample within rigid tubing (Figure A.3a). We then hermetically sealed the tubing using bolted endplates and rubber o-ring gaskets. We designed this mount to contain the applied pressure and ensure air permeated a constant foam cross-section. We then increased the pressure differential across the foam from 0 to 104 kPa (0 to 15 psi) while measuring the flow rate downstream of the sample. We fabricated both soft and rigid foam samples for this measurement: the soft, elastomeric foam was silicone (MM60, Smooth-On; E = 2 MPa, reported) and the rigid foam an epoxy (System 3000, Fibre Glast; E = 16 GPa, reported). Due to the detection limits of our instruments, we required the higher modulus MM60 over MM10 to attain sufficient flow rates for measurement. All foam-fabrication parameters and procedures were unchanged when using

MM60 and System 3000 epoxy. As seen in Figure A.3b, the soft foams exhibited considerably higher flow than the rigid foams. We also observed the expected behavior that for a given material, a higher porosity resulted in a higher flow rate for all applied pressures.

We next compared the experimental airflow measurements with an adapted Kozeny-

Carman (KC) model for fluid flow through a packed particulate bed. The KC model relates fluid flow to key parameters as displayed in Equation 1,

훥푃 훹 퐷 휙 퐴 푄 = ( 1 ) 180 퐿 휂 (1 − 휙)

where Q is flow rate, ΔP is pressure drop across the sample, Ѱ is PDMS sphericity, Dp is the spacing between pores, ϕ is sample porosity, A is the sample cross-sectional area, L is sample length, and η is viscosity of the fluid. We directly measured Q, ΔP, A, and L from the airflow

experiment. We used X-ray µCT to extract Ѱ, Dp, and ϕ for each of the tested foams.

Figure A.3 Airflow through foam actuators. (a) Airflow measurement sample mount, (b) airflow measurements through soft [red] and rigid [blue] foams with KC model prediction of flow behavior [black], and foam microstructure during 0 L min-1 (c) and 7 L min-1 (d) airflow. Highlighted region shows more open pore network in (d) than in (c), where grey is PDMS and black is air-filled pores.

The X-ray µCT scans of both the soft and rigid foam samples yielded cylindrical (radius, r = 1.5 mm and thickness, d = 3 mm) volumetric reconstructions of the foam structure. Using the freely available ImageJ image processing software with the BoneJ170 plugin (version 1.4.0), we determined the porosity, pore surface area, and average spacing between pores from the scans using the Volume Fraction, Isosurface, and Thickness functions, respectively. Since the foam microstructure is relatively similar to that of cancellous bone, the BoneJ plugin is a particularly useful software package.171 Further details of this process are provided in SI. Further, we calculated the sphericity (Ѱ) of PDMS using Equation 2 with measured values of PDMS volume (V) and surface area (S.A.) from BoneJ.

휋 (6푉) ( 2 ) 훹 = 푆. 퐴. The calculated parameters were similar between soft and rigid foams of equal porosity indicating repeatability of the process independent of matrix composition. When input into the KC model, using no free parameters, the predicted flow rates are in close agreement with the measured rates through rigid foams (Figure A.3b). The soft foams, however, exhibited much higher flow rates than both the rigid foams and the flow rate predicted using the KC model. To determine the cause of this discrepancy, we compared µCT scans of the sample with and without air flowing through it. Visually, when air flowed through the foam samples, we noted that the foam cylinder deformed to create hemispherical surfaces in the direction of airflow. The µCT scans were consistent with this behavior in that they showed an apparent 12% increase in porosity when permeating at a 7 L min-1 flow rate relative to the porosity at 0 L min-1 (Figure A.3c,d). We attribute the apparent increase in porosity to the expansion of pores in accommodating the strain of the hemispherical macroscopic deformation. Further verifying this phenomenon, our calculations showed that the porosity was highest in the center of the sample (the region furthest from fixed

edges) and became incrementally less porous in regions closer to the perimeter. As the porosity is a heavily weighted parameter in Equation 1, we attribute the increase in flow through soft foams to this strain-induced porosity increase.

Figure A.4 The foam-based fluid pump design and principle of operation. (a) Fluid pump as cast, (b) fully assembled fluid pump after applying external inextensible shell, (c) X-ray fluoroscope of pump when left chamber is uninflated (left) vs. inflated (right), (d) schematic of pump operation. Green represents an inflated foam chamber while red represents an uninflated chamber. W1 and W2 represent valves in water transporting tubing; A1 and A2 represent valves in air transporting tubing. A red “X” indicates a closed valve. The pump is composed of a pure MM10 top [A], pneumatic chambers composed of MM10 foam [B], a MM60/woven KevlarTM barrier separating the left and right halves [C], pneumatic inputs [D], water-transporting tubing [E], and water chambers [F]. To demonstrate the utility of foam-based soft actuators, we fabricated a functional fluid pump with a biologically inspired external geometry (Figure A.4a,b). This pump is actuated pneumatically (Figure A.4c) and is composed entirely of soft materials (SI text). Prior to use, we attached the pump to a pressurized air source and fully primed it with water. The pump generates water flow using only a single air source and the timed control of four solenoid valves via a

microcontroller (Arduino Uno). We made simple modifications to the microcontroller program to attain a wide range of pumping frequencies. The only electric power required for the pump is that needed to power the controller and valves. Two two-way valves control water flow (W1 and W2 in Figure A.4d; 08F23O2140A3F4C75, Parker) and two three-way valves control air flow and allow venting (A1 and A2; 912-000001-031, Parker). The pump attains water flow by alternating between 2 states: (State 1) valves A1 and W1 are open, valve A2 is venting, and valve W2 is closed; (State 2) valves A2 and W2 are open, valve A1 is venting, and valve W1 is closed (Figure

A.4d). In State 1, air travels from the source through A1 to inflate the left foam chamber. This inflation pressurizes the adjacent left water chamber generating water flow through W1 into the right water chamber. In this state, valve A2 is venting to accommodate compression of the right foam chamber as the right water chamber inflates. The microcontroller then switches all valves to

State 2, causing the right foam chamber to inflate, pressurizing the right water chamber and causing water flow through W2 back to the left water chamber. When pumping water at frequencies of 2

Hz, 1 Hz, and 0.1 Hz, we observed sustained output flow rates of 190 mL min-1, 370 mL min-1, and 430 mL min-1 (MR3L213NV, Key Instruments) at pressures of 20 kPa, 14 kPa, and 12 kPa, respectively (3846K1, McMaster Carr). The 430 mL min-1 flow rate is 80% faster than the previously highest reported rate from a soft pump.165

While pumping, the water flow is pulsatile due to the alternating inflation and venting of each foam chamber; however, throughout each inflation step, the flow is sustained. Therefore, we observed continuous flow within each half cycle (sustained for 10 s at a 1 Hz frequency). This flow is uniquely different than the rapid bursts of flow exhibited by previously reported (i.e. combustion-powered) pumps. To the best of our knowledge, this is the only soft pump that offers sustained flow. Similar to other reported soft pumps, our design is a displacement pump that relies

on compliant diaphragms. Unlike other pumps, however, our design does not employ combustion for inflation. Although combustion is a powerful energy source,172 the complexity in managing the safety and timing is complicated. As our pump undergoes only mechanical loading (and not mechanical combined with significant thermal loading), we expect the pump to have lifetimes comparable to other soft actuators, which have been reported in excess of a million actuation cycles.173

This pump provides an alternative to current ventricular assist devices (VAD) and artificial hearts, both of which are primarily composed of rigid materials. Consisting entirely of soft materials, our pump could easily deform and conform in response to the forces imposed on internal organs. Additionally, the two primary material components of the pump (i.e. PDMS and KevlarTM) are both biocompatible.174,175 In further development of the pump, a flow increase and overall volume reduction will be necessary for its utility as a functional, implantable prosthetic. If used as a VAD, a version of this pump could eliminate the need for the complex impeller mechanisms presently used, which show a propensity to collect blood clots.176 Further, a VAD using a poroelastic foam sleeve would not require boring into the heart itself, reducing complications from surgery.177

A.4 Conclusions

This work demonstrates elastomeric foams as a new material platform for designing compliant machines. Unlike previous soft lithography fabrication methods, these foams provide the unique capability to produce truly three-dimensional actuating structures. Further, because the foams are open-celled, we see a significant reduction in design complexity as there is no need for molded air channels. We also demonstrate that the actuating behavior is easily tailored during formulation by tuning porosity. Using this new material system we created an entirely soft fluid

pump that generates pulsatile, unidirectional flow at physiologically relevant pressures. Further, the pump produces flow rates higher than any soft pump reported.

In their current state of development, these foams have two primary limitations: i) the porous network limits the inflation rate and ii) the internal structure tears when overinflated. The fibrillar PDMS network within the foam presents a tortuous path for airflow which limits actuation rate. This effect is dependent on foam porosity and is much more pronounced in lower porosity samples. Despite this limitation, however, the ϕ = 0.7 porosity foam actuators always demonstrate greater flow rate than a comparable pneu-net design (SI Text).18 Interestingly, at pressures in excess of ΔP ~ 100 kPa (ΔP ~ 15 psi), the poroelastic actuators show more than double the flow rate of our model pneu-net.

In future work, the use of a tougher elastomer will allow higher porosity foams (with less tortuous airflow pathways) that could withstand higher inflation pressures while avoiding rupture.

To further increase the actuation rate, anisotropic and/or oriented fugitive materials could be used to generate pores. We would expect pores with a higher aspect ratio would provide a less tortuous pathway for the inflation fluid and would therefore increase the speed of inflation.

A.5 Experimental Section

A.5.1 Foam Fabrication

We fabricated foams via a lost-salt process using MM10 PDMS unless otherwise noted.

To produce the foams, we first mixed the PDMS prepolymer and NH5CO3 (Alfa Aesar, used as- received) at a desired ratio and allowed the mixture to cure at room temperature. The prepolymer- to-porogen volume ratio dictates the final porosity of the foam. We then placed the cured

PDMS/porogen composite in a vacuum oven at 150°C until the porogen had entirely decomposed.

The porogen typically decomposed in 2-6 hours depending on part size.

A.5.2 Characterization

We performed tensile testing of the foams according to ASTM D412 on a Zwick Roell z010 instrument. We conducted all tests using a 10 kN load cell and a strain rate of 6.25 min-1.

We imaged the internal structure of the foams using an X-ray µCT (ZEISS Xradia Versa

520) and the inflation of the foam using a Philips EasyDiagnost Eleva. Details of the subsequent

µCT image analysis are provided as supporting information.

A.6 Supplemental Information

A.6.1 Thermogravimetric Analysis (TGA)

The collected TGA data reveals several important aspects of the thermal stability of the

system. First, we observed that the pure porogen (NH5CO3) begins thermal decomposition at approximately 50°C and that this behavior is unchanged when mixed with the MM10 PDMS

(Figure A.5a). We also note that the pure PDMS is thermally stable through 250°C. At a constant temperature of 150°C, the porogen decomposed entirely within ~10 minutes (Figure A.5b). Again, we observed similar behavior for the porogen in PDMS. The remaining mass after ~ 20 min corresponds with the initial mass of PDMS.

Figure A.5 Thermogravimetric analysis of foam components. Decomposition curves of (a) PDMS (black), PDMS + porogen (red), and pure porogen (blue) at a ramp rate of 10 °C min-1. (b)PDMS + porogen (black) and porogen alone (red) when held at 150 °C

A.6.2 Blocked Force Measurements

Figure A.6 is an extension of the data presented in Figure A.6c. We observed the same general trend that actuators withstand greater inflation pressures as porosity decreases. We note that the ϕ = 0.5 porous actuators show much greater variability than the ϕ = 0.6 and ϕ = 0.7 porous samples. We attribute this variation to the ϕ = 0.5 porous foam being much closer to the percolation porosity required for an open-cell network and therefore local concentration variations have a greater overall effect on the actuating behavior.

Figure A.6 Blocked force behavior of bending actuators.

A.6.3 Blocked Force of Extending Actuator

In an additional blocked force measurement, our extending actuator provided a force of 20

N when pressurized to 70 kPa with no apparent foam failure. We performed this measurement by sandwiching the actuator between a balance and a rigid, fixed surface. Because the actuating displacement was minimal (only that necessary to depress the balance), the majority of the inflation energy is transferred as this large measured force.

A.6.4 Image Analysis Process

We processed the raw X-ray µCT image stacks using the following custom Matlab thresholding algorithm.

function threshold()

for l=100:900 %picks the 100th to the 900th image if l<10 rawImage=dicomread(['I000',num2str(l),'.dcm']);%reads the images else if l<100 rawImage=dicomread(['I00',num2str(l),'.dcm']); else rawImage=dicomread(['I0',num2str(l),'.dcm']); end end

brightImage=immultiply(rawImage,2);%brightens the image by 2x

binaryImage=im2bw(brightImage(:,:)); %converts brightened image to a binary image

smoothedImage=bwareaopen(binaryImage,40); %smooths black region of the image

invertedImage=imcomplement(smoothedImage); %inverts the smoothed binary image

reSmooth=bwareaopen(invertedImage,1); %smooths the inverted image

threshImage=imcomplement(reSmooth); %re-inverts smoothed image

finalImage=rawImage; %defines final output image

[m,n]=size(rawImage); for i=1:m for j=1:n if rawImage(i,j)>100 if threshImage(i,j)==0 finalImage(i,j)=0; %converts pixel to black in finalImage end if threshImage(i,j)==1 finalImage(i,j)=60000; %converts pixel to white in finalImage end else finalImage(i,j)=20000; %converts background to arbitrary grey value end end end

imwrite(finalImage,['FinalImage_',num2str(l),'.tiff']); %writes Tiff image end

We use the immultiply and bwareaopen parameters to ensure the thresholded images

visibly matched the raw image. We next imported the image stack into ImageJ image analysis software and selected the circular field of view as the region of interest. As Figure A.7a shows, the areas shaded in black represent the foam while the white areas represent the pores.

We measured the average PDMS thickness (i.e. spacing between pores) using the

Thickness function in the BoneJ plugin. This also returns a graphical representation of the foam thickness (Figure A.7b).

To analyze foam porosity, we first invert the binary image stack (Figure A.7c) and run the

Volume Fraction function in BoneJ. Finally, we calculate the PDMS surface area using the

Isosurface function with a resampling parameter of 8 and a threshold of 128. This returns a bone surface (BS) value as well as a 3D graphic result (Figure A.7d).

Figure A.7 Image analysis of µCT images. (a) Thresholded slice, (b) graphical representation of PDMS thickness between pores, (c) inverted thresholded image to determine porosity, and (d) 3D reconstruction of image stack.

A.6.5 Pump Assembly

We first cast the foam chamber component of the pump using a 3D-printed mold (Objet24,

Stratasys, Ltd.) mirroring the external geometry of the bottom half of the human heart. We filled this mold with a PDMS/porogen mixture (MM10; ϕ = 0.7 porogen) and allowed it to cure at room temperature overnight (Figure A.8a, left). Concurrently, we cast PDMS into a separate mold to form the top half of the pump (Figure A.8a, right). After demolding, we placed the foam chamber component in a vacuum oven at 150 °C under continuous vacuum for 8 hours to remove the porogen. At this point, the foam chamber was fully porous (Figure A.8b). We then sealed the foam chamber by brushing PDMS onto the interior and exterior surfaces. Once sealed, we bonded the top and bottom pump halves together using PDMS. During this step, we also inserted pneumatic lines (1.57 mm ID, 2.08 mm OD; 427446, Becton Dickinson) through the top pump half and into the bottom half, embedding them into the foam. Next, we vertically bisected the pump using a scalpel (Figure A.8c) and sealed the newly exposed foam creating the two fully isolated foam

TM chambers. We then impregnated Kevlar woven fabric (10 x 15 cm; 1065, Fibre Glast) with

MM60 and cured the composite at room temperature to create the fluid chamber divider. We then adhered the divider to the two pump halves using MM10 as an adhesive and sealant. The full exterior of the pump was then coated in a mixture of MM60 and chopped carbon fiber (2 inch length; Fibre Glast; 2 wt. % fiber loading) to form an inextensible shell. This shell is essential for efficient pumping as it directs inflation inwards towards the internal fluid chambers. Finally, we completed the assembly by inserting tubing into the fluid chambers and affixing zip ties around the tubing ports to provide a hermetic and watertight seal.

Figure A.8 Molding process to form the pump’s foam shell. (a) Casting molds for lower foam component [left] and PDMS top [right], (b) resulting foam component after porogen removal, and (c) separated pump halves that form the two foam chambers and the two water chambers.

A.6.6 Flow Rate Comparison of Foams to Pneu-net

We compared the soft foam samples presented in Figure A.3 to a model system for pneu- net type actuators. To simulate the limiting air channels within the pneu-net design,18 we used a disc of solid MM10 (radius, r = 1.25 cm and thickness, d = 1.25 cm) with a single, 1 mm diameter

hole through its thickness. The airflow behavior of this sample is compared to the soft foam samples in Figure A.9.

We observed that the ϕ = 0.7 porous foam showed a higher flow rate at all tested pressures signifying a more rapid inflation of actuators composed of this material. We also observed that the model pneu-net system showed differing flow rate increases throughout the tested pressure range.

We attribute the change in slope of this curve to the strain stiffening of MM10. As we increased pressure, we observed the MM10 disc bulging in the direction of flow (similar to what we had observed in the foam samples) increasing the volume of the hollow air channel and reducing flow resistance. The channels, however, eventually stop changing in dimension as the material strain stiffens, reducing the rate of flow increase with pressure.

Figure A.9 Airflow measurement of soft foams and a pneu-net model.

APPENDIX B

SCULPTING SOFT MACHINES*

B.1 Introduction

In the past few years, the field of soft robotics has become a well-defined discipline with practical uses3,178. Research groups have developed actuators, sensors, and robots that have potential use in biomedical devices for surgery and rehabilitation46,49,179–181, in mobility and manipulation for autonomous walking and swimming18,19,34, and as wearable robots45,61,182,183. Due to their compliant materials and manufacturing techniques, soft robots present a number of advantages over conventional ones: safe human-robot interaction, low-cost production20,24,34,61,166, and simple fabrication with minimal assembly, all of which allow their potential fabrication and use in classrooms or small laboratories184–186.

Current state-of-the-art soft robots are often composed of prismatic actuators, an artifact of the replica molding process used to make many of them18,37. To fabricate 3D robots, without complex molding or multiple assembly steps, our lab developed poroelastic foam actuators24. We fabricated these foams by combining silicone elastomer as the base material and ammonium hydrogen carbonate (NH5CO3) as a fugitive porogen. The resulting foams have intrinsic pathways for fluid transport, which enable actuation when sealed and inflated. While useful in a laboratory or industrial environment, one of the product gases—ammonia— is toxic, making the fabrication process unsuitable for classrooms, small laboratories, or artist studios not equipped with exhaust hoods for toxic gases.

In order to increase participation in soft robotics by non-experts (e.g., artists, K-12 students

* Argiolas, A. et al. Sculpting Soft Machines. Soft Robot. 3, 101–108 (2016). Reproduced with permission.

and STEAM members), we present a manufacturing process that builds on our prior work in foams that employs sculpting rather than casting and uses benign table salt (NaCl) as the porogen, allowing fabrication outside of specialized laboratories. We describe the viscoelastic properties of this silicone-salt compound and its ability to be sculpted rather than molded, eliminating the need for expensive tools such as 3D printed molds or milling machines or computer aided design (CAD) software. We report the resulting mechanical properties of the foams (i.e., elastic modulus, ultimate strain, and fluid flux through the pores) along with the capabilities of the assembled actuators (i.e. block force measurements and weight-lifting demonstrations).

B.2 Materials and Methods

B.2.1 Foam manufacturing

Using the lost salt method described previously168, we fabricated the foams by mixing together a widely available silicone pre-polymer (Ecoflex 00-10; Smooth-On, Inc.) and table salt

(Morton Salt, Inc.). We chose Ecoflex 00-10 because of its low elastic modulus, E=50 kPa, and its very high ultimate strain, 휀푢푙푡~8 (manufacturer's data sheet). These properties allow large and reversible deformation. We chose common table salt because of its low health risk, broad availability, and ability to dissolve aqueously. After mixing Ecoflex 00-10 Part A and Part B (1:1 ratio, by weight), we added the predetermined amount of salt to the uncured elastomer and manually mixed the silicone and salt. We based the amount of salt added on the desired porosity. dfdf After mixing Ecoflex 00-10 and salt together, we directly sculpted (or sometimes molded) the mixture into a variety of 3D shapes (Figure B.1a-g). To facilitate sculpting, we increased the viscosity of the mixture by either allowing the silicone to partially cure for 20 minutes at 25 °C or by adding THI-VEX thickener (Smooth-On, Inc.)(4% wt. of Part A), which is able to immediately increase elastomers viscosity and reduce the curing time. We noted that when the mixture cured

fully at room temperature for four hours as prescribed in the Ecoflex 00-10 technical datasheet, a two-layer structure in the foam formed, in which the top layer was composed only of Ecoflex, and the bottom of both Ecoflex and salt (Figure B.1h). To achieve a homogeneous pore distribution, we sped up the curing process by placing the molded/sculpted mixture into an oven at 80 °C. We note, however, that the two-layer foam could be useful in creating a built-in actuation direction or for sealing.

Figure B.1 Fabrication of foam forms. (a-d) Sculpting process. 3D Sculpted examples: (e) hand, (f) Y-shaped gripper and (g) geometric shapes. (h) Ecoflex 00-10 and table salt foam double layer when curing at room temperature.

Once the mixture cured fully, we dissolved the salt in warm water (~50°C) overnight. To speed up dissolution, we used an ultrasonic bath (VWR Model 75T) and periodically stretched

(just few millimeters, <10%) the foams under water to increase salt-to-water contact. After drying the foam, we used compressed air (at flow rates accessible by computer keyboard air dusters) to remove residual salt crystals, which ensured an interconnected fluid pathway by breaking thin walls between closed cells. Figure B.2 shows the foam porous structure. We could further shape the foams with scissors before sealing them with another elastomer.

Figure B.2 Porous structure of elastomer foam.

B.2.2 Foams mechanical tests: tensile tests and air flow rate measurements

To characterize the mechanical properties of the cured foams, without adding THI-VEX thickener, we molded samples with three different porosities: 휙 = 푉푁푎퐶푙 = 0.5,0.6,0.7 푝표푟푒 푉푠푖푙푖푐표푛푒+푉푁푎퐶푙 and performed uniaxial, monotonic tensile tests (3 samples per porosity) according to the ASTM

D412 standard (Figure B.3a). We performed the tests on a Zwick & Roell Z010 at an elongation rate of 50 mm min-1 using a 10 kN load cell. As a reference, we also performed uniaxial tensile tests on pure elastomer (휙푝표푟푒 = 0.0).

Figure B.3 Mechanical testing and airflow measurements. (a) Ecoflex 00-10 and manufactured foams uniaxial tensile tests; (b) flow rate measurements. Towards predicting actuator inflation rates, we performed flow rate measurements through foams with three different porosities. We molded 150 mm long cylindrical samples of diameter 25 mm and cut them into 15 mm lengths. We then glued the samples to the inner surface of rigid acrylic tubes with length and inner diameter of 25 mm using Sil-Poxy silicone rubber adhesive

(Smooth-On, Inc.), leaving 5 mm of space above and below the sample. Next, we mounted each tube between two 3D printed caps and rubber O-rings to make the tube air-tight (Figure B.4). The 90

mount connected the encased sample to a pressurized air source with controllable flow rate. We measured the output flow rate as well as the pressures upstream and downstream of the foam to calculate the pressure drop (using H271A-005, Hedland Inc. and FLDA3422G, Omega Inc., respectively). Our tests covered the range of pressures: 0<∆P<100 kPa (Figure B.3b).

After conducting mechanical tests and flow rate measurements, we chose to fabricate foams with 휙푝표푟푒 = 0.7 porosity because of its higher flow rate and greater ease of sculpting (due to its larger salt-to-elastomer ratio).

Figure B.4 Airflow measurement experimental set-up. (a) Airflow measurements setup. (b) Foam sample housing for airflow measurements details.

B.2.3 Rheological tests

We quantified the flow properties of our pre-foam mixture using oscillatory rheology on a

DHR-3 rheometer (TA Instruments) with a parallel plate tool. Using a salt volume fraction of

휙푝표푟푒 = 0.7, we measured the elastic, G', and loss, G'', moduli as well as complex viscosity, *.

We applied increasing stress, 0.0 푘푃푎 < 휎 < 3.0 푘푃푎, at a constant frequency of  = 1.0 퐻푧 to simulate the estimated stress range and rate experienced during sculpting (Figure B.5a). Finally, we measured the evolution of G', G'', and * as the silicone cured (Figure B.5b). The constancy of

G' over the two-hour test, while the elastomer was curing, indicates that the salt dominates the elasticity, and the viscosity evolution demonstrates the large window of time for sculpting (about

60 minutes). All rheological tests were performed at room temperature.

B.2.4 Soft actuator manufacturing: sealing, bending tests and actuation force measurements

To fabricate these foam actuators, we added both an external seal to trap the inflating fluid and an inextensible strain-limiting layer to direct motion3,20,173. We fabricated multiple actuators sealed with Ecoflex 00-10, Ecoflex 00-30, Ecoflex 00-50, Mold Max 10, OOMOO 30 (All from

Smooth-On), or Elastosil M4601 (Wacker Chemie AG). Table B.1Table 2.1 displays some key mechanical properties of these elastomers.

Ecoflex Ecoflex Mold Max OOMOO Elastosil 00-10 00-30 10 30 M4601 Shore hardness 00-10 00-30 10A 30A 28A Modulus at ε = 1 (MPa) 0.06 0.07 0.24 0.75 1 Elongation at break (%) 800 900 529 250 700 Tensile strength (MPa) 0.83 1.38 3.26 1.65 6.5

Table B.1 Mechanical properties according to manufacturers’ datasheets.

We used paper (40 lb Kraft Paper Roll; Staples) for the inextensible layer (EGPa), as it is easily accessible, low cost, and can be cut to any shape using a laser cutter or scissors. As paper is porous, this layer merges completely with the elastomer while curing. When sealing with lower hardness elastomers (Ecoflex), we reinforced the paper with a thin (2 mm) layer of OOMOO 30

(Figure B.6).

Figure B.5 Rheological behavior of liquid foam precursor. (a) Stress sweep and (b) Time sweep.

We used two different methods to form the external seal: painting and molding. A thin

sealing layer (about 1-2 mm) can be painted, and this is faster (especially for complex shapes) because it eliminates the need to design a mold; however, it can result in an uneven seal. Molding yields reproducible seals and should be used where reproducibility is required. In moldless fabrication, however, we apply the sealing layer with paint, which results in more variation as can be seen in blocking force tests (Figure B.7). The one-step seal cure (by molding or painting) avoids bonding issues between asynchronously cured seal layers, as opposed to the multi-step cure often used in traditional approaches159, as shown in Figure B.8. Though the foam and seal cure at different times, the bond is sufficiently strong for inflation due to the large bonding area available on the foam's porous surface.

B.2.5 Blocked force measurement

We performed blocked force measurements to characterize the actuators' applied force as a function of inflation pressure. We tested 휙푝표푟푒 = 0.7 foams with three sealing elastomers, (Mold

Max 10, M4601, and OOMOO 30) each of which has a higher hardness than Ecoflex 00-10. We used an acrylic sample mount to constrain the bending actuator (30x105x8 mm size) to a constant curvature and a balance to record applied force (Figure B.9). We increased inflation pressure from

0 kPa until the actuator failed (e.g., sealing rupture or bursting). Figure B.7a shows actuation force measurement results for molded actuators, while Figure B.7b shows results for painted actuators.

Figure B.6 Foam actuators with different sealing materials and methods. (a) Casted actuators. (b) Ecoflex 00-10 actuator cross-section. (c) Painted actuators.

Figure B.7 Actuation force measurement. Ecoflex 00–10 ϕpore = 0.7 foam with Mold Max 10, M4601, and OOMOO 30 seal for casted (a) and painted (b) actuators.

B.2.6 Load-Bearing Actuation

Using the actuator sealed with Ecoflex 00-10, we measured the curvature as a function of the inflation pressure. By using a very soft foam and seal, we obtained high bending (curvature radius r = 25 mm) with low pressures (27.5 kPa) (Figure B.10a). Using a different sealant elastomer

(Elastosil M4601) we were able to lift different weights by inflating a similar actuator (Figure

B.10b) in accordance with the actuation force measurements for the selected elastomer (Figure

B.10c).

B.2.7 Bending tests

(Elastosil M4601) we were able to lift different weights by inflating a similar actuator (Figure

B.10b) in accordance with the actuation force measurements for the selected elastomer (Figure

B.10c).

B.3 Results & Discussion

As expected, the foams' elastic moduli decreased as porosity increased (Figure B.3a). Table

2 displays, for each porosity, the average tensile modulus E, ultimate tensile stress 푢푙푡 and ultimate strain 푢푙푡. All the foam samples showed an ultimate breaking strain 푢푙푡 > 3.5. Though this value is less than half the nonporous Ecoflex ultimate breaking strain (푢푙푡  8), it is adequate for fluidic actuation.

Figure B.8 Sealing process for foam actuators. (left) Casting (right) Painting

Figure B.9 Blocking force measurements setup. (a) lateral view; (b) top view.

Figure B.10 Bending Actuator Performance. (a) Bending example of soft block actuator. Foam is sealed with Ecoflex 00–10 and the strain-limiting layer is paper and OOMOO 30; (b) M4601 Actuator test with 100/450/500g weight in accordance with actuation force measurement for M4601 sealing (c), as reported in Figure B.7a. Color images available online at www.liebertpub.com/soro

The flow rate measurements (Figure B.3b) demonstrate that 휙 = 0.7 foam has the highest flow rate, which we attribute to its higher porosity. The figure shows a nearly linear relationship between airflow rate and differential pressure. The sample-to-sample variability is likely due to the stochastic nature of the pore network and foam fabrication variables (salt crystal size, degree of foam stretching, and amount of air pumping to remove residual table salt). All

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porosities tested had a suitable flow rate for fluidic actuation.

Rheological tests confirmed that we can manually sculpt the foams (Figure B.5a) within the mixture sculpting time (Figure B.5b), according to the material rheological properties.

Through our blocked force tests (Figure B.7), we observed that actuation force is related to the mechanical properties of the sealing elastomer, as expected. Specifically, higher hardness seals required greater inflation pressures to initiate actuation and to attain a given endpoint force.

For molded actuators, we recorded actuation initiation pressures of 45 kPa, 55 kPa, and 65 kPa and maximum actuation forces of 4.8 N, 4.9 N, and 4.3 N for Mold Max 10, M4601, and OOMOO

30, respectively. Sculpted and painted actuators inflate at lower pressures, P~25 kPa. We also measured maximum actuation forces of 3.1 N, 3.6 N, and 4.8 N for M4601, OOMOO 30, and

Mold Max 10. In the case of M4601 and OOMOO 30, the lower maximum actuation force is likely due to the longer cure time of these elastomers, resulting in longer flow times and dripping. For painting uniform layers, Mold Max 10 is the best choice.

Figure B.10b shows an actuator with 0.7 porosity foam and M4601 seal raising different weights in accordance to the force-pressure relation in Figure B.7. The inflation pressure necessary to raise the different weights was consistent with the blocked force data in Figure B.10c. We applied internal pressures of P = 100 kPa, 130 kPa, and 145 kPa in an attempt to raise 100 g, 450 g, and 500 g, respectively. The actuator completely lifted the 100 and 450 g weights, but only succeeded in dragging the 500 g about 5 cm along the resting surface. We were not able to increase the inflation pressure in order to raise 500 g because of actuators' failure (rupture, bursting or irreversible deformation) at higher pressures (about 150 kPa).

We fabricated a functional Y-shaped gripper by first sculpting a Y-shaped Ecoflex 00-10 foam with 휙 = 0.7 porosity. We sealed the foam with Ecoflex 00-30 (cured for 30 minutes at

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80°C). Each of the three fingers had dimensions of 200 x 10 x 7 mm, which sufficed to wrap around an apple. The strain-limiting layer was comprised of paper (40 lb Kraft Paper Roll; Staples) and OOMOO 30 reinforcement. After curing, we demonstrated grasping (via pneumatic inflation) and movement of the apple (~200 g; Figure B.11).

Figure B.11 Apple picking with a sculpted, Y-shaped gripper.

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The gripper successfully grasped the object at low inflation pressures (P ≈ 45 kPa). We deliberately used only the foam and a strain-limiting layer to demonstrate the foam's capability as an internal inflation chamber without other mechanical constraints (e.g. external fibers or molded air chambers, as in PneuNet devices). With this approach, we sculpted a functional, monolithically sealed gripper in about 60 minutes that did not require 3D printed molds and used only low cost, readily available materials.

B.4 Conclusions

In this work, we present a new method for moldless manufacturing of soft FEAs and, in general, soft robots. We report mechanical properties and actuation measurements for the proposed foams and actuators. Our approach presents some unique advantages over traditional soft actuator fabrication.

A primary advantage of this manufacturing technique is that our method enables anyone to fabricate soft robots. This process is safe, low cost, and uses easily available materials making it applicable in K-12 classrooms, small laboratories, and art studios. Moreover, this technique enables fully functional 3D machines without a mold. The soft, stretchable, and sculptable porous materials eliminate the need for both molds to form an actuator’s external shape and sacrificial molds to form an internal air chamber. This aspect is notable because it significantly reduces the time and number of fabrication steps necessary to manufacture complex 3D actuators.

Additionally, since our process forms the sealing layer in a single step, our seal does not have the interface (created between asynchronously cured layers) that can be prone to delamination and leaking.

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APPENDIX C

FIBER SELECTION FOR ADDRESSING SENSOR DRIFT IN AN OPTICAL,

PROPRIOCEPTIVE FOAM

C.1 Introduction

In Chapter 3, I present a soft, optical silicone foam that can detect when it is being bent or twisted and the magnitude of the deformation. In Chapter 4, I discuss a problem with the system, which is that model error increases over time. The increase in model error seems to be due to a nonuniform shift in optical fiber intensities. One way to manage this problem is to embed one reliable deformation sensor that does not drift with time and use it to recalibrate the models when needed. However, Chapter 4 shows that to decrease the error without an embedded calibration sensor, we can calculate the mean offset between the original training data and the drifted data and use it to either shift or augment the original training data. This technique did not reduce the error to its original value, however.

We hypothesize that model error may be improved by considering the physical location of each fiber. One way to include spatial information in the training data is to weight each fiber’s intensity values according to their location in the sensor system. Another approach would be to remove certain fibers from the original training data based on location. In this appendix, we consider a more general version of the latter approach.

C.2 Experiments

If some fiber subsets produce models whose error does not increase due to sensor drift, we can search for those fiber sets. As in Chapter 3, we used random search129 and a greedy approach.

For random search, we removed subsets of fibers from the training data and drifted data, trained

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new models, and evaluated those models on the drifted dataset. We performed this process for subset sizes 1 through 26. We did not have the computational capacity to exhaustively search through subsets with sizes 5 through 25, so for these sizes, we randomly tried 28000 different fiber subsets. For the greedy approach, we removed one fiber from the data at a time, choosing the fiber which, when removed, produced a model with the greatest accuracy when compared with the other models of the same feature set size.

C.3 Results

Figure C.1 presents the results from these experiments. For the results from the random search, we plotted the mean error for each subset size (“rand. mean”) and the minimum error found for each subset size (“rand. min”). The results from the greedy search are marked “greedy” on the graphs. For reference, we included the error of the original model on the drifted dataset (“original error” and the error of the augmented model reported in Chapter 4 on the drifted dataset

(“augmented error”). We found that there were several fiber subsets that produced models with decreased error due to drift. For the k-Nearest-Neighbors (kNN) classifier, the best error found was 0.32 using a fiber subset of size 5. This error is an improvement on the best model found through data augmentation, which had an error of 0.47. For the linear model, the best fiber- removed model used a fiber subset of size 21 and had an error of 11.7, compared with the best data-augmented model whose error was 13.6.

C.4 Discussion

These results suggest that feature selection may be a useful way to address error due to sensor drift. When model error increases, this approach could be used to reduce it. These experiments did not show an obvious trend in the fibers that produced the best models, but further experiments might reveal a pattern. If that pattern is independent of the drifted data, and instead

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dependent on location, one could perform feature selection before drift occurs to preemptively combat the error increase. The best linear models used enough fibers to maintain low error prior to drift (according to Figure 3.7 in Chapter 3), suggesting that early feature selection would not greatly increase initial model error. The best kNN model used only 5 fibers, which may be a large enough decrease to affect initial model error; however, the random search found models with comparably low error that used around 10 fibers, which Figure 3.7 shows is a large enough feature set to maintain low initial error.

Figure C.1 Model Error on Drifted Data vs. Feature Set Size. Error bars are standard deviation.

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